Pipe A and B together can fill a tank in 12 minutes. Pipe B and C together can fill the same tank in 15 minutes. Pipe C and A together can fill the same tank in 20 minutes. Firstly pipe C is opened. After 'L' minutes, pipes A and B both are also opened. Remaining tank got filled in 5 minutes. What is the value of L?
Show answer & explanation
Correct answer: B
Explanation
Given:
A + B fill the tank in = 12 minutes
B + C fill the tank in = 15 minutes
C + A fill the tank in = 20 minutes
According to the formula:
Work done in 1 minute = 1 / Time taken
A + B = 1/12
B + C = 1/15
C + A = 1/20
2(A + B + C) = 1/12 + 1/15 + 1/20
= 5/60 + 4/60 + 3/60
= 12/60
= 1/5
A + B + C = 1/10
Now, the rate of C:
C = (A + B + C) − (A + B)
= 1/10 − 1/12
= (6 − 5)/60
= 1/60
Let us assume C works alone for L minutes.
Work done = L/60
Then, A and B are also opened.
Combined rate of the three = 1/10
Work done in 5 minutes = 5/10 = 1/2
L/60 + 1/2 = 1
L/60 = 1/2
L = 30 minutes