Question

The circumference of an inlet pipe and an outlet pipe is 15 cm and 10 cm respectively. How long will it take the tank to be filled, when it is empty and both pipes are opened?
Statement 1: Outlet pipe can empty the tank in 25 minutes
Statement 2: Inlet pipe can fill the empty tank in 56 minutes

• A. If the data in statement (1) alone is sufficient to answer the question
• B. If the data in statement (2) alone is sufficient to answer the question
• C. If the data in both the statements together are needed to answer the question
• D. If either statement (1) alone or statement (2) alone is sufficient to answer the question

Hint:

Circumference ratio 15:10 gives the flow-rate ratio (square of the circumference ratio) before either statement is used.

Answer 1

The Correct Option is D

Step 1: Convert the pipe sizes into a flow rate ratio.
For pipes of the same shape, the amount of water flowing through in a given time is proportional to the cross section area, and area is proportional to the square of the circumference.
The inlet and outlet circumferences are in the ratio \(15:10 = 3:2\), so their flow rates are in the ratio \(3^2:2^2 = 9:4\).
This ratio (inlet rate to outlet rate = 9:4) is available from the question itself, before either statement is used, so it can be paired with just one more fact.

Step 2: Check statement 1 alone.
Statement 1 says the outlet alone empties the full tank in 25 minutes, so the outlet's rate is \(1/25\) of the tank per minute.
Using the 9:4 ratio, the inlet's rate is \((9/4) \times (1/25) = 9/100\) of the tank per minute.
With both pipes open, the net filling rate is \(9/100 - 4/100 = 1/20\) of the tank per minute, so the tank fills in 20 minutes. This is one definite number, so statement 1 alone is sufficient.

Step 3: Check statement 2 alone.
Statement 2 says the inlet alone fills the empty tank in 56 minutes, so its rate is \(1/56\) of the tank per minute.
Using the same 9:4 ratio, the outlet's rate is \((4/9) \times (1/56) = 1/126\) of the tank per minute.
With both pipes open, the net rate is \(1/56 - 1/126\), a single fixed value, so this also gives one definite time to fill the tank. Statement 2 alone is sufficient too.

Final Answer:
Because the question already supplies the rate ratio through the pipe sizes, either statement by itself, combined with that ratio, pins down a filling time. \[ \boxed{\text{d - either statement alone is sufficient}} \]