Aptitude - Time and Work - Discussion

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.

A =20 Days
B=30 Days
C=60 Days

LCM = A,B,C
LCM = 60
A = 60/20 =3.
B = 60/30 = 2.
C = 60/60 =1.

AFTER 3 DAYS B, C JOINED.

Total =3 + 3(3 + 1) = 15 DAYS.

3A----20
2B----30
1C----60 this come from L. C. M------60.

Add:all efficiency A+B+C=3+2+1=6.
Per day works of A+B+C=60/6=10.
3days work of A+B+C.

3 = (3+3per day work of A +6 per day work of a+b+c).
3 = 12(Tw=60 if we want 60in the table of 12 then we need to * ...12*5 and also *right side)
5*3 = 12 * 5.

15day = 60. A can do the work in 15 days.