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Fast trick to solve the pipe and cisterns.

Two pipe 'A' and 'B' can fill a tank in 34 min and 28 min respectively.A water tank 'C' can empty the tank in 17 min . first 'A' and 'B' are opened. After 10 min. 'C' is also opened. In how much time , the tank is full?

STEP 1 :

Both pipe operate in 1 min.= 1 / 34 + 1 / 28 part of tank

Both pipe operate in 10 min.= 10 * ( 1 / 34 + 1 / 28) part of tank

=10 * (14 + 17 / 476 )part of tank

=310 / 476 part of tank

=155 / 238 part of tank

STEP 2 :

Remaining part of tank = 1 - 155 / 238 part of tank

= 83 / 238 part of tank

STEP 3 :

All pipe operate in 1 min. = 1 / 34 + 1 / 28 - 1 / 17

=59 / 476

476 / 59 min = 1 part of tank

STEP 4 :

476 / 59 * 83 / 238 = 83 / 238 part of tank

0.53548387096774 = 83 / 238 part of tank

Tank will be full in 0.53548387096774 min.

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