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1. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?

A. 30 days

B. 40 days

C. 60 days

D. 70 days

Solution:

\begin{aligned} Let A's 1 day's work = x and \\ B's 1 day's work = y \\ Then, x + y = \frac{1}{30} \\ 16 x + 44 y = 1 \\ Solving these two equations, we get \\ x = \frac{1}{60} and y = \frac{1}{60} \\ ∴ B's 1 day's work = \frac{1}{60} \\ Hence, B alone shall finish the \\ whole work in 60 days \end{aligned}

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