Question

3) A can do a piece of work in 10 days and B can do it in 15 days. They worked toghether for 4 days and A left. In how many days can be B finish the remaining work​

Answer 1

Given:

• A can do work in 10 days.
• b can do work in 15 days.
• A and B work together for 4 days and A left.  

To find:

We need to find in how many days B can complete the remaining work.

Solution:

Work done by A = $\frac{1}{10}$

Work done by B = $\frac{1}{15}$

Work done by A and B in one day = $\frac{1}{10} + \frac{1}{15}$  

Here, we need to simply the term using LCM and find the answer.

    = $\frac{1}{10} + \frac{1}{15}$

    $\frac{10 + 15}{150}\\\\ = \frac{25}{150}\\ \\=6$                      

Work done by A and B in one day = 6 days.

Here, A and B done work together in 4 days.

So, we need to find the done by A and B = 6 × 4 ⇒ 24

The work done together by A and B = 24 days.

Here, A left = 24 - 1  ⇒ 23 days.

Now, B can do work if A left = 23 days.

Now, we need to find the work done by B.

Therefore, Work done by B = $\frac{1}{23}$ × $\frac{15}{1}$

Now, we need to eliminate and find the values.

                   Work done by B = $\frac{1}{23}$ × $\frac{15}{1}$

                                                $=\frac{15}{23} \\\\\\= 1 \frac{8}{15}$              

Remaining Work done by B = $1 \frac{8}{15}$ days.