Question

$A$ can do a piece of work in 25 days and $B$ in 20 days. They work together for 5 days and then $A$ goes away. In how many days will $B$ finish the remaining work?

• A. 17 days
• B. 11 days
• C. 10 days
• D. None of these

Answer 1

The correct option is B 11 days

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

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

A's and B's together 1 day's work

$\frac{1}{25}+\frac{1}{20}=\frac{4}{100}+\frac{5}{100}=\frac{4+5}{100}=\frac{9}{100}$

Their 5 day's work together = 5 x 1 day's work

$1-\frac{45}{100}=\frac{100}{100}-\frac{45}{100}=\frac{100-45}{100}=\frac{55}{100}$

Now, this remaining work is done by B.

Let B takes $x$ days to complete it.

$\frac{1}{20}\times x=\frac{55}{100}\Rightarrow x=\frac{55}{100}\times 20\Rightarrow x=\frac{55}{5}\Rightarrow x=11$

Hence, B will finish the remaining work in $11$ days.