Question

Working together, A $\&$ B finish a DTP work in 10 days. Had A worked at half his efficiency and B at 5 times her efficiency, then they would have finished the DTP work in half the scheduled time. In how many days can B complete the DTP work on her own?

• A. 24
• B. 36
• C. 15
• D. 30

Answer 1

The correct option is D 30

Let us solve this using answer options

It is better to start with option (c) or option (d) as it is given that B takes ${\frac{1}{5}}^{th}$ the actual time in the second case. Option (c) and (d) are multiples of 5

Solving for option (c)

$\frac{1}{x}+\frac{1}{15}=\frac{1}{10}\Rightarrow$ A takes 30 days

They would have finished the work in half the time if A takes 60 days and B takes 3 days

But ,$\frac{1}{60}+\frac{1}{3}\ne \frac{1}{5}$. Hence, this is not the answer

Solving for option (d)

$\frac{1}{x}+\frac{1}{30}=\frac{1}{10}\Rightarrow$ A takes 15 days

They would have finished the work in 5 days, if A takes 30 days and B takes 6 days

$\frac{1}{30}+\frac{1}{6}=\frac{1}{5}$. Hence, this is the answer.