Aptitude - Time and Work - Discussion

A->15.
B->20.
LCM of 15,20 is 60.
A can do 4 parts and B can do 3 parts.
A and B together complete 7 parts in 1 day.
for 4 days 28 parts can complete.
60-28 = 32(leftover work).
32/60 = 8/15.

A - 15 days.
B - 20 days.

LCM of 15 & 20 is 60 (The total work is 60 also).

So,

The Efficiency of one day's work is 60/15 = 4 and 60/20 = 3.

Then, both A & B can complete the work in one day is 4+3=7.

They worked for 4 days, so 7x4=28
Work completed in 4days by both A+B=28.
Then, rest work = Total work - Completed work
Rest work = 60-28=32.
32/60 = 8/15
The answer is = 8/15.

Lcm of 15 and 30 = 60 units.
A's per day work = 60/15 = 4units.
B's per day work = 60/20 = 3units.
A+B's per day work = 4 + 3 = 7units.
A and B together do the work in 4 days.
= 4 * 7 = 28units.
Remaining work = 32/60 = 8/15.

LCM of 15,20 = 60
days * efficiency = work so, 15 * 4 = 60 20 * 3 = 60.
Efficiencies are 4+3 =7,
They worked for 4 days 7*4 =28.
Total work =60,
60 - 28 =32.
Then the remaining work = 32/60 = 8/15.

A completed this in 15 days.
Then, A completed this work in 1 days = (1/15).

B completed this work in 20 days
Then, B completed this work in 1 days = (1/20).

Both A and B both completed this work in 1 days = (A+B)
= ((1/15)+(1/20)).
then, the LCM of 15 and 20 is 60;

we get,
((1*4)+(1*3)/60))
= 7/60.

A and B both completed the same work in 4 days = ((7/60)*4)
= 7/15.

Let's take total work is = 1.
then we know that,

Rest work= total work - completed work.
= 1 - (7/15).
= (15-7)/15.
= 8/15 Answer.

How come remaining work 1- 7/15? Please explain me.

4( 1/15 + 1/20 ) = work done by both of them together

Work Done + Work left =1 =>because the work is 100% completed

4( 1/15 + 1/20 ) + work left = 1;
work left = 1 - (28/ 60);
Then, work left = 8/15;

A's 1 day's work = 1/15;
B's 1 day's work = 1/20;

(A + B)'s 1 day's work = (1/15+1/20)= 7/60;

Total days required to complete total work of (A+B) = 60/7,
After 4 days, remaining days left = 60/7 - 4 = 32/7,
Hence, remaining work = 32/7 x 7/60 = 8/15,
Hope it helps.

Please explain, why the remaining work is 1.

Just take LCM on 15 and 20 of 60.
Total work 60.

Capacity A 4 and capacity B 3 total 7.
They both worked together for 4 days and completed work 28.
Remaining work 32/60,
So, the Answer 8/15.