Kalpesh Sharma

==>> A sum of money amounts to Rs.6690 after 3 years and to Rs.10035 after 6 years on compound interest. Find the sum.

Ans: Rs. 4460

Sol: Let the Sum be Rs. P. Then
P [1 + (R/100)]^3 = 6690………..(i)
P [1 + (R/100)]^6 = 10035………..(ii)
On dividing, we get [1 + (R/100)]^3 = 10035/6690 = 3/2.
P * (3/2) = 6690 or P = 4460.
Hence, the sum is Rs. 4460.

==>> Simple interest on a certain sum is 16/25 of the sum. Find the rate percent and time, if both are numerically equal.

Ans: Rate = 8% and Time = 8 years

Sol: Let sum = X. Then S.I. = 16x/25
Let rate = R% and Time = R years.
Therefore, x * R * R/100 = 16x/25 or R^2 = 1600/25, R = 40/5 = 8
Therefore, Rate = 8% and Time = 8 years.

39. Find
i. S.I. on RS 68000 at 16 2/3% per annum for 9 months.
ii. S.I. on RS 6250 at 14% per annum for 146 days.
iii. S.I. on RS 3000 at 18% per annum for the period from 4th Feb 1995 to 18th April 1995.

Ans: i. RS 8500.
ii. RS 350.
iii. RS 108.

Sol:

i. P = 68000, R = 50/3% p.a. and T = 9/12 year = ¾ years
Therefore, S.I. = (P * Q * R/100)
= RS (68000 * 50/3 * ¾ * 1/100) = RS 8500.

ii. P = RS 6265, R = 14% p.a. and T = (146/365) year = 2/5 years.
Therefore, S.I. = RS (6265 * 14 * 2/5 *1/100) = RS 350.

iii. Time = (24 + 31 + 18) days = 73 days = 1/5 year

P = RS 3000 and R = 18% p.a.
Therefore, S.I. = RS (3000 * 18 * 1/5 * 1/100) = RS 108

==>> A sum at simple interest at 13 ½% per annum amounts to RS 2502.50 after 4 years. Find the sum.

Ans: sum = RS 1625

Sol: Let sum be x. Then,
S.I. = (x * 27/2 * 4 * 1/100) = 27x/50
Therefore, amount = (x + 27x/50) = 77x/50
Therefore, 77x/50 = 2502.50 or x = 2502.50 * 50 / 77 = 1625
Hence, sum = RS 1625

==>> The minute hand of a clock overtakes the hours hand at intervals of 65 min of the correct time. How much of the day does the clock gain or lose?

Ans: the clock gains 10 10/43 minutes

Sol: In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60
minutes.
To be together again, the minute hand must gain 60 minutes over the hour hand.
55 minutes are gained in 60 min.
60 min. are gained in [(60/55) * 60] min == 65 5/11 min.
But they are together after 65 min.
Therefore, gain in 65 minutes = (65 5/11 - 65) = 5/11 min.
Gain in 24 hours = [(5/11) * (60*24)/65] = 10 10/43 min.
Therefore, the clock gains 10 10/43 minutes in 24 hours.

==>> A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours. What will be the true time when the clock indicates 1 p.m. on the following day?

Ans. 48 min. past 12.

Sol: Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours.
24 hours 10 min. of this clock = 24 hours of the correct clock.
145/6 hrs of this clock = 24 hours of the correct clock.
29 hours of this clock = [24 * (6/145) * 29] hrs of the correct clock
= 28 hrs 48 min of the correct clock.
Therefore, the correct time is 28 hrs 48 min. after 8 a.m.
This is 48 min. past 12.

==>> At what time between 2 and 3 o’ clock will the hands 0a a clock together?
Ans: 10 10/11 min. past 2.

Sol: At 2 o’ clock, the hour hand is at 2 and the minute hand is at 12, i.e. they are 10
min space apart.

To be together, the minute hand must gain 10 minutes over the other hand.
Now, 55 minutes are gained by it in 60 min.
Therefore, 10 min will be gained in [(60/55) * 10] min = 10 10/11 min.
Therefore, the hands will coincide at 10 10/11 min. past 2.

==>> What was the day of the week on 12th January, 1979?

Ans: Friday

Sol: Number of odd days in (1600 + 300) years = (0 + 1) = 1 odd day.
78 years = (19 leap years + 59 ordinary years) = (38 + 59) odd days = 6 odd days
12 days of January have 5 odd days.
Therefore, total number of odd days= (1 + 6 + 5) = 5 odd days.
Therefore, the desired day was Friday.

==> Find the day of the week on 16th july, 1776.

Ans: Tuesday

Sol: 16th july, 1776 means = 1775 years + period from 1st january to 16th july
Now, 1600 years have 0 odd days.
100 years have 5 odd days.
75 years = 18 leap years + 57 ordinary years
= (36 + 57) odd days = 93 odd days
= 13 weeks + 2 odd days = 2 odd days
Therefore, 1775 years have (0 + 5 + 2) odd days = 0 odd days.
Now, days from 1st Jan to 16th july; 1776
Jan Feb March April May June July
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days
= (28 weeks + 2 days) odd days
Therefore, total number of odd days = 2
Therefore, the day of the week was Tuesday

==>> Find the angle between the minute hand and hour hand of a click when the time is 7.20?

Ans: 100deg

Sol: Angle traced by the hour hand in 12 hours = 360 degrees.
Angle traced by it in 7 hrs 20 min i.e. 22/3 hrs = [(360/12) * (22/3)] = 220 deg.
Angle traced by minute hand in 60 min = 360 deg.
Angle traced by it in 20 min = [(360/20) * 60] = 120 deg.
Therefore, required angle = (220 - 120) = 100deg.

==>> A and B can do a piece of work in 12 days ; B and C can do it in 20 days. In how many days will A, B and C finishes it working all together?

Also, find the number of days taken by each to finish it working alone?

Ans:60 days

Sol: (A+B)’s one day’s work=1/12; (B+C)’s one day’s work=1/15 and (A+C)’s one day’s
work=1/20.
Adding, we get: 2(A+B+C)’s one day’s work = (1/12+1/15+1/20)=1/5.
Therefore, (A+B+C)’s one day’s work=1/10.
Thus, A, B and C together can finish the work in 10 days.
Now, A’s one day’s work
= [(A+B+C)’s one day’s work] – [(B+C)’s one day’s work]
= 1/10-1/15)
= 1/30.
Therefore, A alone can finish the work in 30 days.
Similarly, B’s 1 day’s work = (1/10 -1/20) = 1/20.
Therefore, B alone can finish the work in 20 days.
And, C’s 1 day’s work= (1/10-1/12) = 1/60.
Therefore, C alone can finish the work in 60 days.

==>> A is twice as good a workman as B and together they finish a piece of work in 18
days.In how many days will A alone finish the work?

Ans:27 days.

Sol: (A’s 1 day’s work): (B’s 1 day’s work) = 2:1.
(A + B)’s 1 day’s work = 1/18.
Divide 1/18 in the ratio 2:1.
Therefore A’s 1 day’s work = (1/18 * 2/3) = 1/27.
Hence, A alone can finish the work in 27 days.

==>> 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work?

Ans: 12 ½ days.

Sol: Let 1 man’s 1 day’s work = x and 1 boy’s 1 day’s work =y.
Then, 2x+3y=1/10 and 3x+2y=1/8.
Solving, we get: x=7/200 and y=1/100.
Therefore (2 men +1 boy)’s 1 day’s work = (2*7/200 + 1*1/100) = 16/200 = 2/25.
So, 2 men and 1 boy together can finish the work in 25/2 =12 ½ days.

==>> A man is standing on a railway bridge which is 180m long. He finds that a train crosses the bridge in 20seconds but himself in 8 seconds. Find the length of the train and its speed.

Ans: length of train=120m
Speed of train=54kmph

Sol: Let the length of the train be x meters
Then, the train covers x meters in 8 seconds and (x + 180) meters in 20 seconds.
Therefore x/8 = (x+180)/20 ó 20x = 8(x+180) ó x = 120
Therefore Length of the train = 120m
Speed of the train = 120/8 m/sec = 15 m/sec =15 * 18/5 kmph = 54kmph

==>> A man sells an article at a profit of 25%. If he had bought it at 20 % less and sold it for Rs.10.50 less, he would have gained 30%. Find the cost price of the article?

Ans. Rs. 50.

Sol: Let the C.P be Rs.x.
1st S.P =125% of Rs.x.= 125*x/100= 5x/4.
2nd C.P=80% of x. = 80x/100 =4x/5.
2nd S.P =130% of 4x/5. = (130/100* 4x/5) = 26x/25.
Therefore, 5x/4-26x/25 = 10.50 or x = 10.50*100/21=50.
Hence, C.P = Rs. 50.

==>> A grosser purchased 80 kg of rice at Rs.13.50 per kg and mixed it with 120 kg rice at Rs. 16 per kg. At what rate per kg should he sell the mixture to gain 16%?

Ans: Rs.17.40 per kg.

Sol: C.P of 200 kg of mix. = Rs (80*13.50+120*16) = Rs.3000.
S.P = 116% of Rs 3000= Rs (116*3000/100) = Rs.3480.
Rate of S.P of the mixture = Rs.3480/200.per kg. = Rs.17.40 per kg.

==>> Two persons A and B working together can dig a trench in 8 hrs while A alone can dig it in 12 hrs. In how many hours B alone can dig such a trench?

Ans:24hours.

Sol: (A+B)’s one hour’s work =1/8, A’s one hour’s work =1/12
Therefore, B’s one hour’s work = (1/8-1/12) =1/24.
Hence, B alone can dig the trench in 24 hours.

==> If a man walks at the rate of 5kmph, he misses a train by only 7min. However if he walks at the rate of 6 kmph he reaches the station 5 minutes before the arrival of the train.Find the distance covered by him to reach the station.

Ans:6km.

Sol: Let the required distance be x km.
Difference in the times taken at two speeds=12mins=1/5 hr.
Therefore x/5-x/6=1/5 or 6x-5x=6 or x=6km.
Hence ,the required distance is 6 km

==> Walking 5/6 of its usual speed, a train is 10min late. Find the usual time to cover the journey?

Ans:50 min

Sol: New speed = 5/6 of usual speed
New time = 6/5 of usual time
Therefore, (6/5 of usual time) – usual time = 10min
Therefore Usual time = 50min

==> A train running at 54 kmph takes 20 seconds to pass a platform. Next it takes 12 seconds to pass a man walking at 6 kmph in the same direction in which the train is going. Find the length of the train and the length of the platform.

Ans. length of the train=160m
length of the platform=140 m.

Sol: Let the length of the train be x meters and length of the platform be y meters.
Speed of the train relative to man=(54-6) kmph =48 kmph.
=(48*5/18) m/sec =40/3 m/sec.
In passing a man, the train covers its own length with relative speed.
Therefore, length of the train=(Relative speed *Time)
=(40/3 * 12) m =160 m.
Also, speed of the train=(54 * 5/18) m/sec=15 m/sec.
Therefore, x+y/2xy=20 or x+y=300 or y=(300-160 m=140 m.
Therefore, Length of the platform=140 m.

==>> From height of 8 mts a ball fell down and each time it bounces half the distnace back. What will be the distance traveled?

Ans.: 24

Sol. 8+4+4+2+2+1+1+0.5+0.5+ and etc .. =24

==>> First day of 1999 is Sunday what day is the last day?

Ans.: Monday

==>> Increase area of a square by 69% by what percent should the side be increased.

Ans.: 13

Sol:Area of square=x2
Then area of increase=100+69=169
square root of 169 i.e 13 .

==>> Ten years ago, chandrawathi’s mother was four times older than her daughter. After 10years, the mother will be twice older than daughter. The present age of Chandrawathi is?

Ans.20 years

Sol: Let Chandrawathi’s age 10 years ago be x years.
Her mother’s age 10 years ago = 4x
(4x+10)+10=2(x+10+10)
x=10
Present age of Chandrawathi = (x+10) = 20years

==>> Finding the wrong term in the given series
7, 28, 63, 124, 215, 342, 511

Ans:28

Sol: Clearly, the correct sequence is
2^3 – 1, 3^3 – 1, 4^3 – 1, 5^3 – 1, ……….
Therefore, 28 is wrong and should be replaced by (3^3 – 1) i.e, 26.

==>> In a college ,1/5 th of the girls and 1/8 th of the boys took part in a social camp.What of the total number of students in the college took part in the camp?

Ans: 2/13

Sol: Out of 5 girls 1 took part in the camp
out of 8 boys 1 took part in the camp
so, out of 13 students 2 took part in the camp.
So, 2/13of the total strength took part in the camp.

==>> On sports day,if 30 children were made to stand in a column,16 columns could be formed. If 24 children were made to stand in a column , how many columns could be formed?

Ans. 20

Sol: Total number of children=30*16=480
Number of columns of 24 children each =480/24=20.

==>> Two trains 200mts and 150mts are running on the parallel rails at this rate of 40km/hr and 45km/hr.In how much time will they cross each other if they are running in the same direction.

Ans: 252sec

Sol: Relative speed=45-40=5km/hr=25/18 mt/sec
Total distance covered =sum of lengths of trains =350mts.
So, time taken =350*18/25=252sec.

==>> 5/9 part of the population in a village are males. If 30% of the males are married, the percentage of unmarried females in the total population is:

Ans: (250/9)%

Sol: Let the population =x Males=(5/9)x
Married males = 30% of (5/9)x = x/6
Married females = x/6
Total females = (x-(5/9)x)=4x/9
Unmarried females = (4x/9 – x/6) = 5x/18
Required percentage = (5x/18 * 1/x * 100) = (250/9)%

==>> A radio when sold at a certain price gives a gain of 20%. What will be the gain percent, if sold for thrice the price?

A) 260%
B) 150%
C) 100%
D) 50%
E) None of these

Ans: 260%

Sol. Let x be original cost of the radio.
The solding price = (100+20)x=120x
If , it is sold for thrice the price ,then 3*120x=360x

So, gain percent is (360-100)=260%.

==>> If the Arithmetic mean is 34 and geometric mean is 16 then what is greates number in that series of numbers?

Ans. 64

Sol. Let two numbers be x, y;
Arthmetic mean=34=>( x+y)/2=34
x+y=68
geometric mean=16=>(xy)pow 1/2=16
xy=16*16=256
By trail and error 16*16=64*4

And 64+4/2=34
So the greatest number int hat series is 64.

==>> The diameter of the driving wheel of a bus is 140cm. How many revolutions per minute must the wheel make in order to keep a speed of 66 kmph?

Ans. 250

Sol. Distance to be covered in 1 min=(66*1000)/60 m=1100m
Circumference of the wheel =(2*22/7*0.70)m=4.4m.
So, Number of revolutions per min=1100/4.4=250.

==>> The boys and girls in a college are in the ratio 3:2. If 20% of the boys and 25% of the girls are adults, the percentage of students who are not adults is:??

Ans.78%

Sol: Suppose boys = 3x and girls = 2x
Not adults = (80*3x/100) + (75*2x/100) = 39x/10
Required percentage = (39x/10)*(1/5x)*100 = 78%

==>> Vivek travelled 1200km by air which formed 2/5 of his trip.One third of the whole trip , he travelled by car and the rest of the journey he performed by train. The distance travelled by tain was???

Ans.800km

Sol: Let the total trip be x km.
Then 2x/5=1200
x=1200*5/2=3000km
Distance travelled by car =1/3*3000=1000km
Journey by train =[3000-(1200+1000)]=800km.

=>> A group consists of equal number of men and women. Of them 10% of men and 45% of women are unemployed. If a person is randomly selected from the group. Find the probability for the selected person to be an employee.

Ans:29/40

Sol: Assume men=100,women=100 then employed men & women r (100-10)+(100-45)=145
So probability for the selected person to be an employee=145/200=29/40

=>> Randy's chain of used car dealership sold 16,400 cars in 1998. If the chain sold 15,744 cars in
1999, by what percent did the number of cars sold decrease?

Ans: 4%

Sol. Let percentage of decrease is x , then
16400(100-x)/100=15744
16400-15744=164x
x=656/164=4%

==>> A three digit number consists of 9,5 and one more number . When these digits are reversed and then subtracted from the original number the answer yielded will be consisting of the same digits arranged yet in a different order. What is the other digit?

Sol. Let the digit unknown be n.
The given number is then 900+50+n=950+n.
When reversed the new number is 100n+50+9=59+100n.
Subtracting these two numbers we get 891-99n.
The digit can be arranged in 3 ways or 6 ways.
We have already investigated 2 of these ways.
We can now try one of the remaining 4 ways. One of these is n 95
100n+90+5=891-99n
or 199n =796
so, n=4
the unknown digit is 4.

==>> A farmer built a fence around his 17 cows,in a square shaped region.He used 27 fence poles on each side of the square. How many poles did he need altogether???

Ans.104 poles

Sol. Here 25 poles Must be there on each side .And around four corners 4 poles will be
present. 4*25+4=100+4=104 poles.

==>> On the first test of the semester, kiran scored a 60. On the last test of the semester, kiran scored 75% By what percent did kiran's score improve?

Ans: 25%

Sol. In first test kiran got 60
In last test he got 75.
% increase in test ( 60(x+100))/100=75
0.6X+60=75
0.6X=15
X=15/0.6=25%

***. A cylinder is 6 cms in diameter and 6 cms in height. If spheres of the same size are made from the material obtained, what is the diameter of each sphere?

Ans. 3 cms

***. Mr. and Mrs. Aye and Mr. and Mrs. Bee competed in a chess tournament. Of the three games played:
a) in only the first game were the two players married to each other.
b) The men won two games and the women won one game.
c) The Ayes won more games than the Bees.
d) Anyone who lost game did not play the subsequent game.
Who did not lose a game?

Ans. Mrs. Bee did not lose a game.

***. There are 4 political parties. Day Flight, Eat well, Good Sleep, Deposit Loss. The 3 statements are
a. Either Day Flight or Eat Well will win the election.
b. Day Flight cannot win election.
c. Neither Deposit Loss nor Eat well can win the election.
Only one statement is true while other two are false .who win the election?

Ans. Deposit Loss ( F T F )

***.In a class 80% have passed english,70% passed Hindi 10% didn't passed
either. If 144 students passed both. What is the total strength of the class.

Ans. 240

***. A die is thrown twice what is the probability that you get same number

Ans. 11/36.

***. A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11 mornings and 12 afternoons. How many days did they stay there totally?

Ans. 18

***. Ann, Boobie, Cathy and Dave are at their monthly business meeting. Their occupations are author, biologist, chemist and doctor, but not necessarily in that order. Dave just told the biologist that Cathy was on her way with doughnuts.
Ann is sitting across from the doctor and next to the chemist. The doctor was thinking that Boobie was a goofy name for parent's to choose,but didn't say anything. What is each person's occupation?

Ans. Since Dave spoke to the biologist and Ann sat next to the chemist and across the doctor, Cathy must be the author and Ann the biologist.The doctor didn't speak, but David did, so Bobbie is the doctor and Dave the chemist.

***. The minute and the hour hand of a watch meet every 65 minutes. How much does the watch lose or gain time and by how much?

Ans. Gains; 5/11 minutes

***. The Bulls, Pacers, Lakers and Jazz ran for a contest. Anup, Sujit, John made the following statements regarding results.
· Anup said either Bulls or Jazz will definitely win
· Sujit said he is confident that Bulls will not win
· John said he is confident that neither Jazz nor Lakers will win
When the result came it was found that only one of the above three had made a correct statement. Who has made the correct statement and who has won the contest.

Ans. Sujith; Lakers

***. A man leaves office daily at 7pm. A driver with car comes from his home to pick him from office and bring back home. One day he gets free at 5:30 and instead of waiting for driver he starts walking towards home. In the way he meets the car and returns home on car. He reaches home 20 minutes earlier than usual. In how much time does the man reach home usually?

Ans. 1hr 20min

***. One of Mr. Horton,his wife,their son,and Mr. Horton's mother is a doctor and another is a lawyer.
a)If the doctor is younger than the lawyer, then the doctor and the lawyer are not blood relatives.
b)If the doctor is a woman, then the doctor and the lawyer are blood relatives. c)If the lawyer is a man, then the doctor is a man.
Whose occupation you know?

Ans. Mr. Horton:he is the doctor.

***. Find the least number when divided by 7 gives the reminder 6, when divided by 6 gives reminder 5, when divided by 5 gives reminder 4 and so on....

Ans. 419

***. If a person walks at 4/5th of his usual speed he reaches 40min late. If he walks at his usual speed how much time does he travels.

Ans. 160min

Ex. Let V = his speed, D = distance and T = time so V=D/T (1)
But, (4/5)*V=D/(T+40) (2)

Comparing D, (4/5)*V*(T+40) = V*T solving T=160

--

***. Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrives at their destination 1 hr and 4 hours respectively after passing each other. How much faster is one train from other?

Ans. Twice

***. A train and A Cyclist reach a station every day at the same time. One day the Cyclist starts 20 minutes late from his house. On his way to station the train crosses him at 5 miles before station. The speed of cyclist is 12mph. find the speed of the train.

Ans.60mph

***. Every day a cyclist meets a train at a particular crossing. The road is straight. The cyclist travels with a speed of 10 kmph. One day the cyclist comes late by 25 min and meets the train 5 km from the crossing. What is the speed of the train?

Ans. 60 kmph.

***. A certain type of mixture is prepared by mixing brand A at Rs.9 a kg. with brand B at Rs.4 a kg. If the mixture is worth Rs.7 a kg., how many kgs. of brand A are needed to make 40kgs. of the mixture?

Ans. Brand A needed is 24kgs.

***. In the given figure, PA and PB are tangents to the circle at A and B respectively and the chord BC is parallel to tangent PA. If AC = 6 cm, and length of the tangent AP is 9 cm, then what is the length of the chord BC?

Ans. BC = 4 cm.

***. Three cards are drawn at random from an ordinary pack of cards. Find the probability that they will consist of a king, a queen and an ace.

Ans. 64/2210.

***. A person with some money spends 1/3 for cloths, 1/5 of the remaining for food and 1/4 of the remaining for travel. He is left with Rs 100. How much did he have with him in the beginning?

Ans. 250 Ex. (x/3)+(2x/15)+(8x/60)+100=x

***. Mr. x (got award in 1971) died when his age was 1/59th the year of birth. What was his date of birth?

Ans. 1947 Ex. X+(X/59) > 1971 so X > 1938 Then by trial and error.

***. Grass grows equally thick and in a uniform rate. It takes 24 days for 70 cows and 60 days for 30 cows to eat the whole of the grass. How many cows are needed to eat the grass in 96 days?

Ans. 20
g - grass at the beginning
r - rate at which grass grows, per day
y - rate at which one cow eats grass, per day
n - no of cows to eat the grass in 96 days
g + 24*r = 70 * 24 * y
g + 60*r = 30 * 60 * y
g + 96*r = n * 96 * y
Solving, n = 20.

Ex. From first two equations convert g and r into terms of y. Then put it in equation 3.

***. There N stations on a railroad. After adding X stations on the rail route 46 additional tickets have to be printed. Find N and X.

Ans. x=2 and N=11 Initially, N (N-1) = t after adding, (N+X)(N+X-1) = t+46

***. There are some chickens in poultry. They are fed with corn. One sack of corn will come for 9 days. The farmer decides to sell some chicken and wanted to hold 12 chickens with him. He cuts the feed by 10% and sack of corn comes for 30 days. So initially how many chicken are there?

Ans. 36

Ex. Let there were originally N chickens.
Corn eaten by 1 chicken in 1 day = 1/(N*9)
After, Corn eaten by 1 chicken in 1 day = 1/(12*30) = 1/360

1/(N*9) = 1/360 + ((1/360)*0.1)

***. 15 men take 21 days of 8 hrs. Each does a piece of work. How many days of 6 hrs each would it take for 21 women if 3 women do as much work as 2 men?

Ans. 30

Ex. One hour’s work = 1/(15*21*8)
Assume X days requires for women to do work.
One hour’s work = 1/(21*X*6)
Comparing one hour’s work, we get X=20 days.
But 2 men work = 3 women work so X = (20*3)/2 = 30

***. If on an item a company gives 25% discount, they earn 25% profit. If they now give 10% discount then what is the profit percentage.

Ans. 50%

***. Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 15 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled?

Ans. 167 minutes. Ex. In 3 minutes it fills 0.017 so in 165 minutes it fills 0.935 and then in 2 minutes A and B fills 0.05+0.033, so it full.

***. There are two circles, one circle is inscribed and another circle is circumscribed over a square. What is the ratio of area of inner to outer circle?

Ans. 1:2
Ex. area of inner circle = PI*r*r
Area of outer circle = PI*a*a where a=root(2)*r

***. A works thrice as much as B. If A takes 60 days less than B to do a work then find the number of days it would take to complete the work if both work together?

Ans. 22½days

Ex. Let, B takes X days to do a work. So A takes X-60 days.
Now A works thrice, so 3(X-60) = X. By solving we get X=90

A works in 1 day = 1/30
B works in 1 day = 1/90
If they work combine, work done in 1 day = 1/30+1/90 = 4/90
So, the work will be completed in 90/4 days.

***. It takes Mr. Kathie y hours to complete typing a manuscript. After 2 hours, he was called away. What fractional part of the assignment was left incomplete?

Ans. (y – 2) / y

Ex. To type a manuscript Kathie took y hours.
Therefore his speed in typing = 1/y.
He was called away after 2 hours of typing.
Therefore the work completed = 1/y * 2.
Therefore the remaining work to be completed = 1 – 2/y.
(i.e.) work to be completed = (y-2)/y

***. There are 3 persons Allan, Bell, and Crag. Allan lent car to Bell and Crag as many as they had already. After some time Bell gave as many cars to Allan and Crag as many as they have. After sometime Crag did the same thing. At the end of this transaction each one of them had 24. Find the cars each originally had.

Ans. Allan had 39 cars, Bell had 21 cars and Crag had 12 cars.

Ex. Allan Bell Crag

Finally 24 24 24
Before Crag’s transaction 12 12 48
Before Bell’s transaction 6 42 24
Before Allan’s transaction 39 21 12

***. It was calculated that 75 men could complete a piece of work in 20 days. When work was scheduled to commence, it was found necessary to send 25 men to another project. How much longer will it take to complete the work?

Ans. 30 days.

Ex. Before:
One day work = 1 / 20
One man’s one day work = 1 / (20 * 75)
Now:
No. Of workers = 50
One day work = 50 * 1 / (20 * 75)

The total no of days required to complete the work = (75 * 20) / 50 = 30

***. A man bought a horse and a cart. If he sold the horse at 10 % loss and the cart at 20 % gain, he would not lose anything; but if he sold the horse at 5% loss and the cart at 5% gain, he would lose Rs. 10 in the bargain. What is the amount paid by him?

Ans. Cost price of horse = Rs. 400 & the cost price of cart = 200.

***. A contractor agreeing to finish a work in 150 days employed 75 men each working 8 hours daily. After 90 days, only 2/7 of the work was completed. Increasing the number of men by __ each working now for 10 hours daily, the work can be completed in time.

Ans. 150 men.

Ex. One day’s work = 2 / (7 * 90)
One hour’s work = 2 / (7 * 90 * 8)
One man’s work = 2 / (7 * 90 * 8 * 75)

The remaining work (5/7) has to be completed within 60 days, because the total number of days allotted for the project is 150 days.

So we get the equation (2 * 10 * x * 60) / (7 * 90 * 8 * 75) = 5/7 where x is the number of men working after the 90th day.

We get x = 225
Since we have 75 men already, it is enough to add only 150 men.

All Aptitude Question's Answer below mentioned.

1. I bought a car with a peculiar 5 digit numbered license plate that on reversing could still be read. On reversing value is increased by 78633.Whats the original number if all digits were different?

2. A family I know has several children. Each boy in this family has as many sisters as brothers but each girl has twice as many brothers as sisters. How many brothers and sisters are there?

3. No. of animals is 11 more than the no. of birds. If the no. of birds were the no. of animals and no. of animals were the no. of birds( ie., interchanging no.s of animals and birds.), the total no. of legs get reduced by one fifth (1/5). How many no. of birds and animals were there?

4. Light glows for every 13 seconds. How many times did it glow between 1:57:58 and 3:20:47 am?

5. There are six boxes containing 5, 7, 14, 16, 18, 29 balls of either red or blue in color. Some boxes contain only red balls and others contain only blue.One sales man sold one box out of them and then he says, " I have the same number of red balls left out as that of blue ". Which box is the one he sold out?

6. There is a 4-inch cube painted on all sides. This is cut down into of 1-inch cubes. What is the no of cubes, which have no pointed sides?

7. There is an element, which triplicates in every hour. Each of these 3
items intern reproduce exactly 3 other items. If a single compound is kept in a
container at noon and the container is full by midnight. After how many hours is the container 1/3 full?

8. The average age of 10 members of a committee is the same as it was 4 years ago, because a young member has replaced an old member. Find how much younger is the new member?

9. A man ate 100 bananas in five days, each day eating 6 more than the previous day. How many bananas did he eat on the first day?

10. A monkey starts climbing up a tree 20ft. tall. Each hour, it hops 3ft. and slips back 2ft. how much time would it take the monkey to reach the top?

11. A person walking 5/6 of his usual rate is 40 minutes late. What is his usual time?

12. There is a circle whose diameter is equal to the length of a chessboard. If that is put on the chessboard how many complete squares will be in the circle.

13. What is the sum of the first 25 natural odd numbers?

14. How big will an angle of 1.5 degree look through a glass that magnifies things three times?

15. A fast typist can type some matter in 2 hours and a slow typist can type it in 3 hours. If both types combine, in how much time will they finish?

16. A rectangular plate with length 8 inches, breadth 11 inches and thickness 2 inches is available. What is the length of the circular rod with diameter 8 inches and equal to the volume of the rectangular plate?

17. What is a percent of b divided by b percent of a?

Answers :

Ans 1. Only 0 1 6 8 and 9 can be read upside down. The answer as 10968
Ans 2. 4 boys and 3 girls.
Ans 3. birds: 11,animals: 22
Ans 4. 383 + 1 = 384
Ans 5. Total no of balls = 89 and (89-29 /2) = 60/2 = 30 and also 14 + 16 = 5 + 7 + 18 = 30
Ans 6. 8
Ans 7. 11:00pm
Ans 8.40 years.
Ans 9. Eight.
Ans 10.18 hours.
Ans 11. 3 hours, 20 minutes. Ex. Solve x*t = (5/6)*x*(t+40)
Ans 12. 32.
Ans 13. 625 Ex. The sum of the first n natural odd Nos. is square (n).
Ans 14. 1.5 degrees (the glass cannot increase the magnitude of an angle.)
Ans 15.1 hr 12 min
Ex. The fast typist's work done in 1 hr = 1/2
The slow typist's work done in 1 hr = 1/3
If they work combine, work done in 1 hr = 1/2+1/3 = 5/6
So, the work will be completed in 6/5 hours. i.e., 1+1/5 hours = 1hr 12 min
Ans 16.3.5 inches
Ex. Volume of the circular rod (cylinder) = Volume of the rectangular plate
(22/7)*4*4*h = 8*11*2 h = 7/2 = 3.5
Ans 17. 1 Ex. a percent of b divided by b percent of a: ((a / 100)*b)/(b/100) * a))=1

**** Please Fill up below Series.
S M T W T _ _

**** Write Anything Here __________________

**** formula true with one stroke 5 + 5 + 5 = 550

Answer :

**** S M T W T F S
Sunday Monday Tuesday Wenseday Thirsday Friday Saturday

**** Anything

**** 5 4 5 + 5 =550

*** A can have a piece of work done in 8 days, B can work three times faster than the A, C can work five times faster than A. How many days will they take to do the work together?

Ans. 8/9 days

*** Two trains move in the same direction at 50 kmph and 32 kmph respectively. A man in the slower train observes the 15 seconds elapse before the faster train completely passes by him. What is the length of faster train?

Ans. 75m

Ex. Length of faster train = Distance traveled by faster train in 15 sec -
Distance traveled by slower train in 15 sec

*** Two cars are 15 Km apart. One is turning at a speed of 50kmph and the other at 40kmph. How much time will it take for the two cars to meet?

Ans. 3/2 hours

*** There are two candles of equal lengths and of different thickness. The thicker one lasts of six hours. The thinner 2 hours less than the thicker one. Rajesh lights the two candles at the same time. When he went to bed he saw the thicker one is twice the length of the thinner one. How long ago did Rajesh light the two candles?

Ans. 3 hours. Ex. (1-(x/6) = 2*(1-(x/4)) Ex. (x/6) = 2*(x/4)

*** In a group of 15,7 have studied Latin, 8 have studied Greek, and 3 have not studied either. How many of these studied both Latin and Greek?

Ans.3

*** In the 4 digits 1,2,3,4 how many 4 digit numbers are possible which are divisible by 4? Repetitions are allowed.

Ans. 64

*** Pipe A can fill in 20 minutes and Pipe B in 30 minutes and Pipe C can empty the same in 40 minutes. If all of them work together, find the time taken to fill the tank?

Ans. 17 1/7 minutes Ex. (N/20 + N/30 – N/40) = 1

*** A boat travels 20 km upstream in 6 hrs and 18 Km downstream in 4 hrs. Find the speed of the water current?

Ans. 7/12 km/h Ex. (20/6 + x) = (18/4 - x)
*** Rice is now being sold at Rs. 20 a kg. During last month its rate was Rs. 16 per kg. By how much percent should a family reduce its consumption so as to keep the expenditure fixed?

Ans. 20 %. Ex. 4 Rs/Kg Increase. So she reduce 4 Rs. Rice = 200 gms

*** Father's age is three years more than three times the son's age. After three years, father's age will be ten years more than twice the son's age. What is the father's present age?

Ans. 33 years.

*** There are 20 poles with a constant distance between each pole. A car takes 24 second to reach the 12th pole. How much will it take to reach the last pole?

Ans. 41.45 seconds the dist. between two poles = x Hence 11x: 24 -> 19x: ?

*** At 6'o a clock ticks 6 times. The time between first and last ticks is 30 seconds. How long does it tick at 12'o clock.

Ans. 66 sec.

*** Three friends divided some bullets equally. After all of them shot 4 bullets the total number of bullets remaining is equal to the bullets each had after division. Find the original number divided.

Ans. 18
Initially. x x x
Now x-4 x-4 x-4
Equation is 3x-12 = x

*** A ship went on a voyage. After it had traveled 180 miles a plane started with 10 times the speed of the ship. Find the distance when they meet from starting point.

Ans. 200miles.
Distance traveled by plane = 1/10 distance traveled by ship + 180

*** Fifty minutes ago if it was four times as many minutes past three o’clock, how many minutes is it to six o'clock?

Ans. Twenty-six minutes.

*** There are 6 volumes of books on a rack kept in order (i.e. vol.1, vol. 2 and so on). Give the position after the following changes were noticed.
All books have been changed
Vol.5 was directly to the right of Vol.2
Vol.4 has Vol.6 to its left and both weren't at Vol.3's place
Vol.1 has Vol.3 on right and Vol.5 on left
An even numbered volume is at Vol.5's place
Find the order in which the books are kept now.

Ans. 2, 5, 1, 3, 6, and 4

1. If a and b are positive integers and (a-b)/3.5 = 4/7, then

Ans. b <>

2. In June a baseball team that played 60 games had won 30% of its game played. After a phenomenal winning streak this team raised its average to 50%. How many games must the team have won in a row to attain this average?

Ans. 24 Ex: 18+n = (60+n)/2

3. In a class composed of x girls and y boys what part of the class is composed of girls?

Ans. x/(x + y)

4. M men agree to purchase a gift for Rs. D. If three men drop out how much more will each have to contribute towards the purchase of the gift?

Ans. 3D/(M²-3M)

5. The price of a product is reduced by 30%. By what percentage should it be increased to make it 100%.

Ans. 42.857% Ex: 0.7 + (0.7*X) = 1

6. There is a square of side 6cm. A circle is inscribed inside the square. Find the ratio of the area of circle to square.

Ans. 11/14

7. An equilateral triangle of sides 3 inch each is given. How many equilateral triangles of side 1 inch can be formed from it?

Ans. 9

8. Each side of a rectangle is increased by 100% .By what percentage does the area increase?

Ans. 300% Ex: (100% = 2 times as 4 times = 300%)

9. Perimeter of the back wheel = 9 feet, front wheel = 7 feet on a certain distance, the front wheel gets 10 revolutions more than the back wheel. What is the distance?

Ans. 315 feet.

10. X% of Y is Y% of?

Ans. X

11. If an item costs Rs.3 in '99 and Rs.203 in '00.What is the % increase in price?

Ans. 200/3 Ex: % of increase = Amount of increase / original amount

12. The price of sugar increases by 20%, by what % should a housewife reduces the consumption of sugar so that expenditure on sugar can be same as before?

Ans. 16.66%

13. If an item costs Rs.3 in '99 and Rs.203 in '00.What is the % increase in price?

Ans. 200/3 Ex: % of increase = Amount of increase / original amount

14. 5 men or 8 women do equal amount of work in a day. A job requires 3 men and 5 women to finish the job in 10 days how many women are required to finish the job in 14 days.

Ans. 7

15. A simple interest amount of Rs 5000 for six month is Rs 200. What is the annual rate of interest?

Ans. 8%

16. In objective test a correct answer score 4 marks and on a wrong answer 2 marks are cut. A student scores 480 marks from 150 questions. How many answer were correct?

Ans. 130.

17. What is the angle between the two hands of a clock when time is 8:30?

Ans. 75

18. If a=2/3b, b=2/3c, and c=2/3d what part of d is b?

Ans. 4/9

19. Successive discounts of 20% and 15% are equal to a single discount of

Ans. 32%

20. If x/y=4 and y is not '0' what % of x is 2x-y

Ans. 175% (2x-y)/x

21. A company contracts to paint 3 houses. Mr. Brown can paint a house in 6 days while Mr. Black would take 8 days and Mr. Blue 12 days. After 8 days Mr. Brown goes on vacation and Mr. Black begins to work for a period of 6 days. How many days will it take Mr. Blue to complete the contract?

Ans.11 Ex. (8/6)+(6/8)+(n/12)=3

22.There are 200 questions on a 3 hr examination. Among these questions are 50 mathematics problems. It is suggested that twice as much time be spent on each math’s problem as for each other question. How many minutes should be spent on mathematics problems?

Ans.72 Ex: (n*50)+((n/2)*150)=180 where n=minute for 1 math question

After a long time, exploring various aspects of blogging I am now finally starting a Blog. :)I was really very keen of writing in public. but I had fear about what to write and what not. But finally the day came where I am going to initiate this task.