Question

Three pipes A, B and C can fill a tank in 6 hours, 9 hours and 12 hours respectively. B and C are opened for half an hour, then A also opened. the time taken by the three pipes together to fill the remaining part of the tank is​

Answer 1

Answer:

Three pipes A, B and C can fill a tank in 6 hours, 9 hours and 12 hours respectively. B and C are opened for half an hour, then A is also opened. The time taken by the three pipes together to fill the remaining part of the tank is :

[A]2 hours

[B]2.5 hours

[C]3 hours

[D]3.5 hours

2.5 hours

Part of the tank filled by pipe B and C in half an hour

= \frac{1}{2}\left ( \frac{1}{9}+\frac{1}{12} \right )

= \frac{1}{2}\left ( \frac{4+3}{36} \right ) = \frac{7}{72}

Remaining part = 1- \frac{7}{72} = \frac{72-7}{72} = \frac{65}{72}

Part of the tank filled by three pipes in an hour

= \frac{1}{6}+\frac{1}{9}+\frac{1}{12}

= \frac{6+4+3}{36} = \frac{13}{36}

∴ Time to fill remaining part

= \frac{65}{72}\times \frac{36}{13} = \frac{5}{2} = 2\frac{1}{2}\ hours

Hence option [B] is correct answer.