Question

A and B can do a piece of work in 24 days. After they have worked together for 15 days, B leaves and A completes the remaining work in 15 days. In how many days B alone do the work?
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Answer 1

Answer :-

A and B can do a piece of work in 24 days.

Let us assume that the total amount of work = 24 units

So , A and B together can complete

$= \frac{24}{24} = 1 \: unit \: per \: day$

Then ,

$A + B = 1 \\ B = 1 - A \: - - - - 1$

After they have worked together for 15 days, B leaves...

So , work done in 15 days

$= 15 \times 1 = 15 \: units$

Remaining work

$= 24 - 15 = 9 \: units \:$

A completes the remaining work in 15 days

A completes the 9 units work in 15 days

so , in one day A completes

$= \frac{9}{15} = 0.6 \: unit \: per \: day$

A = 0.6

Put this in equation 1

$B = 1 - A \\ B = 1 - 0.6 \\ B = 0.4 \: unit \: per \: day$

We have to find in how many days B alone do the work?

So , total amount of work = 24 units

B complete 0.4 unit per day

Then ,

$= \frac{24}{0.4} = 60 \: days$

B alone can complete the work in 60 days

Answer 2

Answer:

Step-by-step explanation:A and B can do a piece of work in 24 days.

Let us assume that the total amount of work = 24 units

So , A and B together can complete

Then ,

After they have worked together for 15 days, B leaves...

So , work done in 15 days

Remaining work

A completes the remaining work in 15 days

A completes the 9 units work in 15 days

so , in one day A completes

A = 0.6

Put this in equation 1

We have to find in how many days B alone do the work?

So , total amount of work = 24 units

B complete 0.4 unit per day

Then ,

B alone can complete the work in 60 days