Problem on Time and Work

Question: A can finish a work in 18 days and B can do the same work in 15 days.B worked for 10 days and left the job.In how many days,A alone can finish the remaining work?

Solution:

Workdone by A in ‘1’ day =1/18
Workdone by B in ‘1’ day =1/15

From question:

B worked for 10 days and how many days A alone finish the remaining work,

Since B worked for 10 days,
Workdone by B in ‘10’ days =10/15

So we have to find the remaining work need to be finished,
Remaining work need to be finished =1-(10/15)=1-(2/3)=(3-2)/3=1/3
Remaining work=1/3
This remaining work (i.e) need to be finished by ‘A’alone which is asked in question

Given that ,

A can finish 1 work in 18 days .
But here remaining work is only 1/3.
So, A finish 1/3 work in 18*(1/3)=18/3=6 days

Therefore, A alone can finish the remaining work in 6 days.

Tips:

For example a person named B has ability to finish a work in 15 days,
Workdone by B in ‘1’ day =1/15
Workdone by B in ‘2’ days =2/15
Workdone by B in ‘3’days=3/15
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For example to find the remaining work:

To find the remaining work ,when B left the work in 2 days,
Workdone by B in ‘2’ days =2/15
Remaining work =1-(2/15)=13/15
Remaining work=13/15
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To find the remaining work ,when B left the work in 3days,
Workdone by B in ‘3’ days =3/15
Remaining work =1-(3/15)=12/15
Remaining work=12/15

Also see:

Time and Work
Different Problem on Time and Work