Aptitude - Time and Work - Discussion

Use unity rule at the last step,
1/5 work is done in = 3 days.
1 work (whole work) is done in = 3/1/5 = 3*5= 15 days.

Worker - TotalDay - OneDay
A - 20 - 1/20
B - 30 - 1/30
C - 60 - 1/60

1st Day - A.
2nd Day- B.
3rd Day - A, B, C.

They said A lonely can work for 2 day.
2A = 2(1/20) =1/10.

Then in third day A, B, C together;
(A+B+C) = 1/20+1/30+1/60,
= 1/10.

3 Days(not 3rd Day) work is;
=2A + (A+B+C).
= 1/10+1/10.
3Days =1/5 work,
6Days =2/5 work,
9Days =3/5 work,
12Days=4/5 work,
15Days= 5/5 =1 work completed.

A work in one day = 1/20,
B work in one day = 1/30,
C work in one day = 1/60.

As A work for 2 days and then on third day B and C do work.

Total work done in three days = A 3 days work+B 1-day work+ C one day work,
= 3/20 + 1/30 + 1/60,
= 9/60 + 2/60 + 1/60
= 12/60.

Total work is done in three days =1/5.
3 = 1/5part.

Let x days required to complete work = 1 part.

3/x = 1/5/1.
x = 3 * 5 = 15 days.

3 days 1/5.
6 days 2/5.
9 days 3/5.
12 days 4/5.
15 days 5/5( work completed).

How did we get 6/60? Anyone explain about it.

Here's an easy one:

Let's assume that the total work is done in x days.

Then x/3 days, A will require B and C's help and 2x/3 days A will be working alone.
So the equation becomes:
x/3(1/20) + 2x/3(1/20 + 1/30 + 1/60) = 1 [1 because 1 unit of work is done in x days].

Solve it and you'll get x = 15. Thanks!

How can you take A's 2 days work? Can anyone explain this pls?

@Keerthi.

We are not directly multiplying.

We just use the unitary method. Here the total work done is 1. In fact, in all these sums total work is 1.

Now,
Since 1/5th of the work is done in 3 days,
Therefore, 1 of the work( whole work) is done in 3*5 days.

Hope you understand.

why are we multiplying 1/5 *3 in the last step? Please explain anyone.

Step 1: Work is done by A+B+C in one day can be calculated as 1/20 + 1/30 + 1/60 = 1/10.
Step 2: For the first two days only A is doing work alone so the work is done by A in two days will be 2*1/20= 1/10.
Step 3: Now total work is done in 3 days by A B & C will be = 1/10+1/10= 1/5.
Step 4: But we need a complete work to be done so we have to convert 1/5 to 1 therefore if we do 1/5 work 5 times then work will be completed (1/5 x 5=1).

Therefore 5 x 3 = 15.

Hope you will understand this solution.