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1. A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?

A. 23 days

B. 37 days

C. $37 \frac{1}{2}$ days

D. 40 days

Solution:

\begin{aligned} Whole work is done by A in \\ = 20 \times \frac{5}{4} = 25 days \\ Now, (1 - \frac{4}{5}) i . e ., \\ \frac{1}{5} work is done by A and B in 3 days \\ Whole work will be done by A and B in \\ = (3 \times 5) = 15 days \\ A's 1 day's work = \frac{1}{25}, \\ (A + B)'s 1 day's work = \frac{1}{15} \\ ∴ B's 1 day's work \\ = \frac{1}{15} - \frac{1}{25} = \frac{4}{150} = \frac{2}{75} \\ So, B alone would do the work in \\ \frac{75}{2} = 37 \frac{1}{2} days \end{aligned}

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