Question

A alone can complete a work in 32 hours and B alone in 24 hours. Starting with A, they work during alternate hours. The total work will be completed in how many hours?

• A. 24 hours
• B. 27 hours
• C. 26.5 hours
• D. 27.5hours
• E. None of these

Answer 1

The correct option is D

27.5hours

(A + B)'s 2 hour's work = $(\frac{1}{32}+\frac{1}{24})=\frac{7}{96}$

Work done in 13 pairs of hours = $(\frac{7}{96}\times 13)=\frac{91}{96}$, Remaining work = $(1-\frac{91}{)}96)=\frac{5}{96}$

Work done by A on 27th hour = $\frac{1}{32}$.

$\therefore$ Remaining work = $\frac{5}{96}-\frac{3}{96}=\frac{1}{48}$

Work done by B in 1 hr = $\frac{1}{24}$

Time needed by B to complete $\frac{1}{48}$ work = 0.5 hours

$\therefore$ Total time taken for work = 27.5 hours.