Question 44

A tank of capacity 1000 cubic centimeter is being filled with water by 3 pipes A, B and C. The areas of cross-section of the pipes A, B and C are“in the ratio 3: 2: 4. Water is flowing through each of these pipes at a different rate in cm/min.twas found that the time taken to fill the tank which was initially empty by the pipes A, B and individually is 20 minutes, 50 minutes and 25 minutes respectively. Find the ratio of the-rates of flow of water through the pipes A and C.

Solution

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Let us say that the cross section areas of A, B, and C are 3a, 2a, and 4a.

Now, assume that the water flows at the rate of x, y, and z per min for each of the pipes respectively.

The amount of water flowing through the pipes (per min) shall be: 3ax, 2ay, 4az

Now, the time taken by each of them to fill the tank is 20 min, 50 min, and 25 min.

This means, 3ax$$\times\ $$20 = 4az$$\times\ $$25, or 100:60, or 5:3

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