Aptitude - Time and Work - Discussion

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

@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.

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

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

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

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.

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.

Solution:

A do a piece of work in = 1/20 days.
'A' work alone for 2 days, so the work done by A on the second day is = 2/20 = 1/10
On the third day, A is assisted by B&C, then the work done by three of them is = 1/10 + 1/20 + 1/30 = 3/20.

Total work done by A in 3 days is = 1/20 + 3/20 = 1/5.

As we have to find number of days, so,

1/5 part of work done by A is in = 3 days.
1 part of the work done by A is in = 3x5 = 15 days.

In 15 days, A can do the work if he is assisted by B& C on the third day.