Pipe A and B together can fill a tank in 16 minutes. Pipe B and C together can fill the same tank in 20 minutes. Pipe C and A together can fill the same tank in 24 minutes. Firstly pipe C is opened. After 'L' minutes, pipes A and B both are also opened. Remaining tank got filled in 4 minutes. What is the value of L?
Show answer & explanation
Correct answer: C
Explanation
Given:
A + B fill the tank = 16 minutes
B + C fill the tank = 20 minutes
C + A fill the tank = 24 minutes
C runs first for L minutes
Then A, B, and C together fill the remaining tank in 4 minutes.
A + B = 1/16
B + C = 1/20
C + A = 1/24
(A + B) + (B + C) + (C + A) = 1/16 + 1/20 + 1/24
= (15 + 12 + 10) / 240
= 37/240
2(A + B + C) = 37/240
A + B + C = 37/480
Part filled in 4 minutes = 4 × (37/480) = 37/120
C filled first in L minutes.
C = (B + C) − B
B = (A + B) − A
First, find A.
A = (A + B + C) − (B + C)
A = 37/480 − 1/20
= 37/480 − 24/480
= 13/480
Now B
B = 1/16 − A = 30/480 − 13/480
= 17/480
Now C
C = 1/20 − B
= 24/480 − 17/480
= 7/480
C completed the work in L minutes = L × 7/480
Total work
L × 7/480 + 37/120 = 1
L × 7/480 + 148/480 = 480/480
L × 7/480 = 332/480
7L = 332
L = 332/7 minutes