Question

Three pipes A, B and C are connected to a tank. Out of the three, A and B are the inlet pipes and C
is the outlet pipe. If opened separately, A fills the tank in 10 hours and B fills the tank in 30 hours. If
all three are opened simultaneously, it takes 30 minutes extra than if only A and B are opened.
How much time does it take to empty the tank if only C is opened?
A. 120 hours
B. 160 hours
C. 140 hours
D. 170 hours​

Answer 1

1/10+1/30-1/x=1/8
1/10+1/30-1/8=1/x
(12+4-15)/120=1/x
1/120=1/x
So x=120
A is the correct answer

Answer 2

Three pipes A , B and C are connected to a tank.

Out of three, A and B are the inlet pipes and C is the outlet pipe. If opened separately, A fills the tank in 10 hours and B fills the tank in 30 hours. If

all three are opened simultaneously, it takes 30 minutes extra than if only A and B are opened.

How much time does it take to empty the tank if only C is opened.

A fills the tank in 10 hrs.

B fills the the tank in 30 hrs.

∴ (A + B) fills the tank = 1/(1/10 + 1/30) = 300/40 = 15/2 hrs

let C empties the tank in x hrs.

now, (A + B + C) fills the tank in 1/(1/10 + 1/30 - 1/x) hrs

a/c to question,

time taken by (A + B + C) - 30 minutes = time taken by (A + B)

⇒1/(1/10 + 1/30 - 1/x) - 1/2 = 15/2

⇒1/(4/30 - 1/x) = 16/2 = 8

⇒4/30 - 1/x = 1/8

⇒1/x = 4/30 - 1/8 = (16 - 15)/120 = 1/120

⇒x = 120 hrs

Therefore the time taken by C to empty the tank is 120 hrs. hence option (A) is correct choice.