Kalpesh Sharma

***. 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.