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 :
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
$latex = \frac{1}{2}\left ( \frac{1}{9}+\frac{1}{12} \right )&s=1$
$latex = \frac{1}{2}\left ( \frac{4+3}{36} \right ) = \frac{7}{72}&s=1$
Remaining part $latex = 1- \frac{7}{72} = \frac{72-7}{72} = \frac{65}{72}&s=1$
Part of the tank filled by three pipes in an hour
$latex = \frac{1}{6}+\frac{1}{9}+\frac{1}{12}&s=1$
$latex = \frac{6+4+3}{36} = \frac{13}{36}&s=1$
∴ Time to fill remaining part
$latex = \frac{65}{72}\times \frac{36}{13} = \frac{5}{2} = 2\frac{1}{2}\ hours&s=1$
Hence option [B] is correct answer.