Aptitude - Time and Work - Discussion

First of all, thank you to explain the method.

I have a doubt that how we know to take (i.e Total work = 60)?

Anyone, please help me to get it.

Thank you for giving the clear explanation @Swetha.

And 60 will come, No of days LCM

15 days to 15 * 4 = 60.
20 days to 20 * 3 = 60.

So, the LCM is 60.

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.

How (1/15+1/20) = 7/60? Please explain me.

@All.

As 1 is the whole work, so when we subtract 7/15 from 1.
Then,
LCM of 1 and 15 will be 15 ( in 1 the denominator will be 1 ).
So, 15-7/15 is 8/15.

@all
(1/15+1/20) =7/60.
Solution:
We have to use the mixed fraction method in a simple way using cross multiplication so it becomes (15+20)/300.
The reason for the 300 came we use the denominator direct multiplication (15*20=300)
Then 15+20 = 35,
Divide:35/300.
It becomes 7/60.

Please explain, why the remaining work is 1.

Just take LCM of 15 and 20 you will get total work of 60.

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.

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.