A, B and C are three pipes connected to a tank. A and B together fill the tank in 6 h, B and C together fill the tank in 10 h and A and C together fill the tank in 12 h. In how much time A, B and C fill up the tank together?

A) 9 h

B) \( \Large 5\frac{3}{7} \) h

C) \( \Large 5\frac{2}{7} \) h

D) \( \Large 5\frac{5}{7} \) h

Correct answer:
D) \( \Large 5\frac{5}{7} \) h

Description for Correct answer:
Part filled bv (A + B) in 1 h = \( \Large \frac{1}{6} \)

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

Part filled by (A + C) in 1 h = \( \Large \frac{1}{12} \)

Part filled by 2 (A + B + C) in 1 h

= \( \Large \frac{1}{6}+\frac{1}{10}+\frac{1}{12} = \frac{10+6+5}{60}=\frac{21}{60}=\frac{7}{20} \)

Therefore, Part filled by (A + B + C) in 1 h

= \( \Large \frac{7}{2 \times 20}=\frac{7}{40} \)

Therefore, Required time = \( \Large \frac{40}{7}=\frac{5}{7} \)


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