Aptitude - Time and Work - Discussion

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

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.

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.

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.

Thanks everyone for explaining the answer.

@Jyoti.

It's 1 -7/15 as it is asking how much work is left. Which means 1 is the total amount of work, and 7/15 is the amount of work completed.

So, to get the remaining work we hv to subtract the work done by the whole work. Which is
1-7/15.
= 15/15 - 7/15.
= 15-7/15.
= 8/15.
Hope it helps.

I am not getting. How 1-7/15? Explain, please.

How 1-7/15? Explain.

LCM of A's and B's:
A-15
B-20.

LCM is 60 (It is also total Work) and Efficiency is TOTAL WORK/ TIME i.e.
60/15 = 4 <<<A's 1 day Efficiency
60/20 = 3 <<<B's 1 day Efficiency.

Combining both 1-day Efficiency then we get 4+3=7 (It means A and B can do 7 units in 1 day)

According to the question:
if they have 7 unit Efficiency they work for 4 days then we get:

7 x 4 and divide by total work (60).
7 x 4/60= 7/15 << it is the part of work they will finish in 4 days.

But the question was asked about how much fraction is left then simply we know that total work is 1 then subtract total work 1-7/15.

We get 8/15 that is the answer.

A+b 1 days work =7/60.