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1. A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?

A. 11 days

B. 13 days

C. $20 \frac{3}{17}$ days

D. None of these

Solution:

\begin{aligned} Ratio of times taken by A and B \\ = 100 : 130 = 10 : 13 \\ Suppose B takes x days to do the work \\ Then, 10 : 13 :: 23 : x \\ \Rightarrow x = \frac{23 \times 13}{10} \\ \Rightarrow x = \frac{299}{10} \\ A's 1 day's work = \frac{1}{23} \\ B's 1 day's work = \frac{10}{299} \\ (A + B)'s 1 day's work \\ = \frac{1}{23} + \frac{10}{299} \\ = \frac{23}{299} \\ = \frac{1}{13} \\ ∴ A and B together can complete \\ the work in 13 days . \end{aligned}

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