Question

A and B completes a work in 25 and 20 days respectively. Both worked together for 5 days and A left. In how many days B completed the remaining work.?

Answer 1

Answer:

B completed the remaining work in 11 days

Step-by-step explanation:

A completes work in 25 days

Thus, A's 1 day work $=\frac{1}{25}$

Also, B complete work in 20 days

Thus, B's 1 day work $=\frac{1}{20}$

Total work is LCM of 20 and 25 $\hspace{0.1cm}=100\hspace{0.1cm}parts$

A's 1 day work $=\frac{100}{25}\hspace{0.1cm}=4\hspace{0.1cm}parts$

B's 1 day work $=\frac{100}{20}\hspace{0.1cm}=5\hspace{0.1cm}parts$

(A + B)'s 1 day work $=\hspace{0.1cm}4 + 5 = \hspace{0.1cm}9\hspace{0.1cm}parts$

Given that both A and B worked together for 5 days

Thus, work completed in 5 days $=\hspace{0.1cm}9 \times 5 = \hspace{0.1cm}45\hspace{0.1cm}parts$

Now, Work remaining $=\hspace{0.1cm}100 - 45 = \hspace{0.1cm}55\hspace{0.1cm}parts$

We know, B's completes 5 parts in 1 day

Thus, B completes 55 parts in $\frac{55}{5}\hspace{0.1cm}=\hspace{0.1cm} 11\hspace{0.1cm}days$

Thus, B completed the remaining work in 11 days