Problems on Time and Work: CAT Quantitative Aptitude

This article takes you through the problems of Time, Work & Wages. This is an important topic and CAT has given questions in the past exams, though as is the practice in CAT, the questions have not been directly based on the formulae.
Let us go through the following problems and solutions!

Example:

If A can complete a work in 12 days, B in 5 days, then find the time (in days) taken by them in each of the cases listed below :

 (a) When and   work together.

 (b) When  and   work alternatively, and work is started by A.

 (c) If   starts two days later, in comparison to A

Solution:

 (a) A's efficiency =

 (b) B's efficiency =

Combined efficiency =

So, the required time when A and B work together =

(b) Assuming the work is started by A on the first day and then followed by B on the second day, in every two days  and  will have a combined efficiency

                                      = 15% (combining A's and B's efficiency from above So in 12 days they will complete

                                         So in 12 days they will complete

= 6 x 15% = 90% 

(we multiply by 6 therefore we consider work done by A and B on alternate days hence for 12 days we take 6 days combined efficiency for A and B)

On the 13^th day,  will finish  of the remaining (i.e.,10% work) and the rest 1.66% will be finished by B on the 14th day by taking time =

Thus, total required time to complete the work =

In this case, A alone works for 2 days before B joins him, which means if A’s efficiency is taken for first 2 days, we get

So, the remaining

therefore Time taken together

                                       this will be less tha 6 days)

Thus, the total required time 

Example:

A contractor has two parallel contracts, contract 1 and contract 2, on which work needs to be finishedin a specified number of days. He puts all his group of workers on contract 1. To be able to finish contract2 also on time he withdraws one worker each day, from second day onwards, from work on contract 1.

Work on contract 1 finishes when the last worker is withdrawn. Had no worker been withdrawn at any stage, work on contract 1 would have finished in   of the time it actually took to finish the work. What is the total number of workers in the contractors group?

[1] 5

[2] 10

[3] 15

[4] 20

Solution:

This is a tricky, but a very easy problem.

Had all the workers worked and no worker was withdrawn, then the work would have finished in 55% of the time it actually took to finish…this means:

If the work was to be finished without withdrawing any man it would take 55 Man-Days but, 1 man was withdrawn everyday beginning 2^ndday of work,  it has taken 100 Man-Days Now, 100 Man-Days can be had, if 10 Men work for 10 days (and no man is withdrawn from work) Also, if 10 men start the work and a man is withdrawn everyday beginning 2nd day…this will mean:

StatementMan-Days

On day 1 there are 10 men working        (10 Man-Days)

On day 2 there are 9 men working          (9 Man-Days)

On day 3 there are 8 men working          (8 Man-Days)

:      :     :     :     :    :

:      :     :     :     :    :

:      :     :     :     :    :

On day 1 there is 1 man working             (1 Man-Day)

This means the contractor had a total of 10 men in his group.

Therefore, the correct option is [2].