Time & Work Level 3 Practice Questions for CAT - 11 July 2014

Ques 1. Mahesh takes twice the time taken by Ramesh to complete a job. Ramesh takes twice the time taken by Suresh to complete the job. Suresh takes twice the time taken by Naresh to complete the job. Two of the four when working together take 50% less of the time taken by the other two together to complete the job. Find these two.

Solution - Let the time taken by Naresh to complete the job is t days.

Then the time taken by Suresh to complete the job is 2t days.

Then the time taken by Ramesh to complete the job is 4t days.

Then the time taken by Mahesh to complete the job is 8t days.

Time taken by Naresh & Ramesh to complete the job would be - 

1/((1/t) + (1/4t)) = 4t/5 days

Time taken by Mahesh & Suresh to complete the job would be - 

1/((1/8t) + (1/2t)) = 8t/5 days

Answer - Naresh and Ramesh

Ques 2. Alok takes m times the time taken by Bola and Chetan to complete a job. Bola takes m times the time taken by Alok and Chetan to complete the job. Chetan takes m times the time takes by Alok and Bola to complete the job. Find m.

Solution - Let the time taken by Alok to complete the job is a days.

Let the time taken by Bola to complete the job is b days.

Let the time taken by Chetan to complete the job is c days.

So according to first condition - 

(1/b) + (1/c) = m/a        Equation 1

So according to second condition - 

(1/a) + (1/b) = m/c       Equation 2

So according to third condition - 

(1/a) + (1/c) = m/b       Equation 3

Adding (Equation 1, Equation 2 & Equation 3) and solving we get,

Answer is m = 2

Ques 3. Two men, three women and three boys can complete a job in 20 days. Four men and nine women can complete the same job in 10 days. Find the ratio of the time taken by a woman and a boy to complete the job.

Solution - Let the unit of work done by 1 man in 1 day is m units. 

Let the unit of work done by 1 woman in 1 day is w units. 

Let the unit of work done by 1 boy in 1 day is b units. 

So the units of work completed by two men, 3 women and 3 boys in 20 days would be = (2m+3w+3b)20 and the units of work completed by four men and nine women in 10 days would be = (4m+9w)10.

As the work done in both the cases is equal - 

(2m+3w+3b)20 = (4m+9w)10

60b = 30w

w/b = 60/30 = 2

Answer - As the ratio of the efficiency of a woman and a boy is 2/1 therefore the ratio of the time taken by them to complete the same work is 2.

Ques 4. Sixty men can do a piece of work in 10 days. The same work is now done in the following manner. On the first day one man starts the work and from the second day onwards one more man joins the group on each day. If the work is completed in this fashion, in how many days will the work be completed?

Solution - Let 1 man do 1 unit of work in one day.

So 60 man in ten days would do 60*10*1 = 600 units of work.

On first day units of work completed is 1

On second day units of work completed is 2

On third day units of work completed is 3 and so on......

So in the first 34 days the work completed would be = 1+2+3+4+5..................34 = 34*35/2 = 595 units of work.

The remaining 5 units of work would be completed on the 35th day in 1/7th of the day.

Answer - The work would be completed in 34 1/7 days.