Three pipes A, B and C can together fill a tank in 8 hours. After working at it together for 2 hours, B is closed and A and C fill the remaining part in 9 hours. Determine the time in which pipe B alone can fill the tank.

Three pipes A, B and C can together fill a tank in 8 hours. After working at it together for 2 hours, B is closed and A and C fill the remaining part in 9 hours. Determine the time in which pipe B alone can fill the tank.

A + B + C together fill the tank in 8 hours

So, rate of (A + B + C) = [1/8] tank per hour

Work done by A + B + C in 2 hours = 2 × 1/8 =[ 1/4 ]tank  

Remaining work = 1 − 1/4 = [3/4 ]tank

Remaining [3/4] tank is filled by A + C in 9 hours

So, rate of (A + C) = 3/4 × 1/9 = 1/12 tank per hour

Rate of B = Rate of (A + B + C) − Rate of (A + C)

= 1/8 − 1/12

= 3/24 − 2/24 =[ 1/24 [tank per hour

 Time taken by B alone = 24 hours

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pipes problem, cbse 12th applied maths old board exam question paper 2025 2026