There are two inlets A and B connected to a tank. A and B can fill the tank in 16 h and 10 h, respectively. If both the pipes are opened alternately for 1 h, starting from A, then how much time will the tank take to be filled?

A) \( \Large 13\frac{1}{4} \)
B) \( \Large 11\frac{6}{8} \)

C) \( \Large 12\frac{2}{5} \)
D) \( \Large 12\frac{1}{4} \)

Correct answer:
C) \( \Large 12\frac{2}{5} \)

Description for Correct answer:
Part filled by A in 1 h = \( \Large \frac{1}{16} \)

Part filled by B in 1 h = \( \Large \frac{1}{10} \)

Part filled by (A+B) in 2 h

= \( \Large \frac{1}{16}+\frac{1}{10}=\frac{13}{80} \)

Part filled by (A+ B) in 12 h = \( \Large \frac{6 \times 13}{80} = \frac{78}{80} \)

Therefore, Remaining part = \( \Large 1 - \frac{78}{80}=\frac{2}{80} = \frac{1}{40} \)

Total time taken by A to fill \( \frac{1}{40} \) part of the tank

= \( \Large \frac{1}{40} \times 16 = \frac{2}{5}h \)

Therefore, Total time taken = \( \Large \left(12+\frac{2}{5}\right) = 12\frac{2}{5}h \)

Please provide the error details in above question

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