Previous Year Questions

Let time taken by pipe P and Q alone to fill the tank is 'P' and 'Q' while the time taken by R alone to empty the tank is 'R.

(1/P) + (1/Q) = (1/14.4) ...... (1)

(1/P) + (1/Q) - (1/R) = (1/18) ..... (2)

From (1) and (2):

(1/14.4) - (1/R) = (1/18)

(1/R) = (1/14.4) - (1/18)

R = 72 minutes

Quantity I:

Let time taken by pipe S alone to fill the tank = S

(1/P) + (1/Q) + (1/S) = (1/8) ..... (3)

From (1) and (3):

(1/14.4) + (1/S) = (1/8)

(1/S) = (1/8) - (1/14.4)

S = 18 minutes

Now,

Time taken by R and S together to fill the tank = 1/[(1/18) - (1/72)]

= 24 minutes

Quantity II:

From equation (1):

[1/P] + [1/(P + 12)] = (1/14.4)

28.8P + 172.8 = P² + 12P

P² - 16.8P - 172.8 = 0

P = 24

Now, time taken by P and R together to fill the tank = 1/[(1/24) - (1/72)]

= 36 minutes

Hence, Quantity I < Quantity II