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Q.

An empty tank can be filled by pipe A in 2 hours and by pipe B in 3 hours. If the two pipes are opened for 1 hour each alternately with first opening of pipe A, then the tank will be filled in :

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a

$2 (\frac{1}{3}) hours$

b

$2 hours$

c

$1 (\frac{1}{2}) hours$

d

$2 (\frac{1}{5}) hours$

answer is A.

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Detailed Solution

A and B can fill the tank

$\begin{array}{l} = \frac{1}{2} + \frac{1}{3} = \frac{3 + 2}{6} = \frac{5}{6} p a r t \to f o r 2 h o u r s \\ Remaining p a r t = 1 - \frac{5}{6} = \frac{1}{6} p a r t \\ \frac{1}{6} p a r t c a n b e f i l l e d b y A \\ \frac{1}{6} \times 2 \Rightarrow \frac{1}{3} minute \\ ∴ t o t a l t i m e \Rightarrow 2 h o u r s + \frac{1}{3} minute \\ \Rightarrow 2 \frac{1}{3} h o u r s \end{array}$

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