TheNightKing wrote:
Pipe A and Pipe B together can fill the tank in 60 min. Efficiency of Pipe A , B and C are in the ratio of 2 : 3 : 1. Pipe A and Pipe B are the inlet pipes whereas Pipe C is the outlet pipe. Find out the time taken by A and C together to fill the tank?
(a) 240 min
(b) 280 min
(c) 300 min
(d) 320 min
(e) 360 min
Hi
Swarna6387 , the key here is the rate of C is negative but I'll break it down step by step first.
Let us set the variables A, B, C as the respective rates. From the first sentence, we can get A and B have a combined rate of 1/60 (job per minute). Hence A + B = 1/60.
We also know A:B = 2:3, we can solve for A and B this way: split the total into 5 equivalents, then A has two pieces and B has three pieces among the five.
\(\frac{1}{60}/5 = 1/300\).
\(A = 1/300 * 2 = 1/150 \)
Next, C is mentioned as an outlet pipe. This means C is working against A and B, and C has a negative rate. The magnitude of the rate of C is half of A, so C = -1/300.
Finally, the combined rate of A and C is \(A + C = 1/150 - 1/300 = 1/300\). Therefore it takes 300 minutes to fill the tank.
Ans: C
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