Two pipes A and B can fill a cistern in 9 minutes and 12 minutes respectively. Both pipes are opened alternatively for 1 min each starting with A. In which time will they fill the cistern ?

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$8 (\frac{3}{4}) minutes$

$14 (\frac{1}{2}) minutes$

$10 (\frac{1}{4}) minutes$

$12 (\frac{3}{4}) minutes$

answer is C.

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Detailed Solution

A can fill a cistern in = 9 minutes $\Rightarrow$ 1 for 1 minute $= \frac{1}{9}$

B can fill a cistern in = 12 minutes $\Rightarrow$ for 1 minute $= \frac{1}{12}$

1. For 2 minutes both can fill $\Rightarrow \frac{1}{9} + \frac{1}{12} = \frac{4 + 3}{36} = \frac{7}{36}$

2. For another 2 minutes can fill $\Rightarrow 2 \times \frac{7}{36} = \frac{14}{36} = \frac{7}{18} p a r t$

3. For another 2 minutes can fill $\Rightarrow \frac{14}{36} + \frac{7}{36} = \frac{21}{36}$

4. For another 2 minutes can fill $\Rightarrow \frac{28}{36}$

5. And another 2 minutes can fill $\Rightarrow \frac{35}{36}$

$Remaining \Rightarrow 1 - \frac{35}{36} = \frac{1}{36}$

$\frac{1}{36} p a r t i s f i l l e d b y A \Rightarrow \frac{1}{36} \times 9 \Rightarrow \frac{9}{36} = \frac{1}{4} minutes$

$∴ T o t a l t i m e = 5 \times 2 + \frac{1}{4} = 10 \frac{1}{4} minutes$

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