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1. A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:

A. 20 days

B. $22 \frac{1}{2}$ days

C. 25 days

D. 30 days

Solution:

\begin{aligned} Ratio of times taken by A and B = 1:3 \\ The time difference is (3 - 1) 2 days \\ while B take 3 days and A takes 1 day . \\ If difference of time is 2 days, B takes 3 days . \\ If difference of time is 60 days, \\ B takes (\frac{3}{2} \times 60) = 90 days \\ So, A takes 30 days to do the work . \\ A's 1 day's work = \frac{1}{30} \\ B's 1 day's work = \frac{1}{90} \\ (A + B)'s 1 day's work \\ = \frac{1}{30} + \frac{1}{90} = \frac{4}{90} = \frac{2}{45} \\ ∴ A and B together can do the work in \\ \frac{45}{2} = 22 \frac{1}{2} days \end{aligned}

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