Aptitude - Time and Work - Discussion

As per the question, A works all days but on every three days A gets assisted by B&C.


Upon calculation through LCM method the total workdays =60 and also with the help of LCM it is possible to find A's & B+C each day work i.e. 60/20 =3, [60/30+ 60/60].

Thus A's efficiency for one day work is 3 and B+C =2+1 =3. On every 3days A finishes 9 work but as he is assisted by B&C on every 3rd day their work also gets added with A's work as a result of which in every 3rd day 9+3=12 work gets completed.

Hence as on every 3rd day, 12 work gets completed the entire work of 60 would be completed by [60*3] /12 =15 days.

Solution:

A's 3 days work = 3/20.
(B+C)'s 3rd day or 1 day work= 1/20.
(A+B+C)'s 3 days work = (3/20+1/20).
= 1/5.

A's 1/5 part work in 3 days.
1 part ---> 15 days.

A can do the wok in 15 days (Ans).

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.

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.

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!

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