Previous Year Questions

M, N, and O together can fill the tank = 120/11 minutes

P and R together can fill the tank = 140 minutes

O, P, and Q together can fill the tank = 84/5 minutes

P, Q, and R together can fill the tank = 280/3 minutes

O and Q together can fill the tank = 420/19 minutes

So, P alone can fill the tank = 1/ (5/84 - 19/420) = 70 minutes

So, Q alone can fill the tank = 1/ (3/280 - 1/140) = 280 minutes

So, R alone can fill the tank = 1/ (3/280 - 1/70 - 1/280) = -140 minutes

Q first, followed by R, and then P,

In three minutes, part of tank filled = 1/70 + 1/280 - 1/140 = 3/280

So, in 92 * 3 = 276 min, part of tank filled = 92 * 3/280 = 69/70

So, remaining part = 1 - 69/70 = 1/70

Thus, in next 1 min Q can fill = 1/280 part

So, remaining part = 1/70 - 1/280 = 3/280

In next 1 min R will empty = 1/140 part

So, remaining part = 3/280 + 1/140 = 1/56

So, in next 1 min P will fill = 1/70 part

Thus, remaining part = 1/56 - 1/70 = 1/280

Now, the remaining part will be filled by Q in 1 min.

Hence, total time = 276 + 1 + 1 + 1 + 1= 280 minutes