Question

two pipes A and B can fill a tank in 12 and 16 minutes respectively. both pipes are opened together, but 4 minute before the tank is full, pipe A is closed. in how many minutes will the tank be full.​

Answer 1

Answer:

64/7 minutes OR 9.14 minutes

Step-by-step explanation:

Let Ra and Rb be rate of pipe A and B respectively

Time taken by A = 12 min

Time taken by B = 16 min

Total volume of tank be LCM(12,16) = 48 units. We took volume as LCM so that to have Rates of A and B as integers.

Using, Rate × Time = Work

Ra = 48/12 = 4 units/min

Rb = 48/16 = 3 units/min

Ra + Rb = 7 units/min = Rab

Using, Rate × Time = Work

Vab(Volume of tank filled when both pipes are open) = Rab × (t - 4) = 7 × (t - 4) = 7t -28 (t is total time taken to fill the tank)

Vb(Volume of tank filled when pipe B runs for 4 mins) = Rb × 4 = 3 × 4 = 12 units

Now,

Vab + Vb = 48

7t -28 + 12 = 48

7t = 64

t = 64/7 = 9.14 min

Time taken by tank to be full will be 64/7 minutes OR 9.14 minutes