Question
Two pipes P and Q can fill tank A in 36 minutes and 72
minutes respectively and empty pipe M can empty the tank in 54 minutes. Tank A has the capacity of 216 liters. If all three pipes opened in tank B for (x – 48) minutes together they filled 60 liter of the tank which is 25% of the quantity of tank B. Find in x minutes what portion of tank B filled, if all pipe P and Q and M opened alternatively in each minute starting with P, followed by Q and M respectivelySolution
For tank A- Pipes P – 36 min, Q – 72 min & M=- 54 min Total quantity = 216 units Efficiency of P = 216/36 = 6 units/min Efficiency of Q = 216/72 = 3 units/min Efficiency of M = 216/54 = (- 4) units/min According to the questions: For tank B — 6 (x – 48) + 3 (x – 48) – 4 (x – 48) = 60 6x – 288 + 3x – 144 – 4x + 192 = 60 5x = (288 + 144 + 60 – 192)    x = 300/5 = 60 minutes Total quantity of tank B = 60 × 4 = 240 liter Alternatively (P + Q – M) for 60 minutes, means each pipe for 20 minutes— All three in 14 minutes (P + Q – M) = 20 × 6 + 20 × 3 – 20 × 4 = 100 liters    Filled portion = 100/240 = 5/12
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