Pipe & Cisterns

Fast trick to solve the pipe and cisterns.

Two pipe 'A' and 'B' can fill a tank in 38 min and 30 min respectively.A water tank 'C' can empty the tank in 13 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 / 38 + 1 / 30 part of tank

Both pipe operate in 10 min.= 10 * ( 1 / 38 + 1 / 30) part of tank

=10 * (15 + 19 / 570 )part of tank

=340 / 570 part of tank

=34 / 57 part of tank

STEP 2 :

Remaining part of tank = 1 - 34 / 57 part of tank

= 23 / 57 part of tank

STEP 3 :

All pipe operate in 1 min. = 1 / 38 + 1 / 30 - 1 / 13

=506 / 3705

3705 / 506 min = 1 part of tank

STEP 4 :

3705 / 506 * 23 / 57 = 23 / 57 part of tank

0.67647058823529 = 23 / 57 part of tank

Tank will be full in 0.67647058823529 min.