Question:hard

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

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Circumference ratio 15:10 gives the flow-rate ratio (square of the circumference ratio) before either statement is used.
Updated On: Jul 21, 2026
  • If the data in statement (1) alone is sufficient to answer the question
  • If the data in statement (2) alone is sufficient to answer the question
  • If the data in both the statements together are needed to answer the question
  • If either statement (1) alone or statement (2) alone is sufficient to answer the question
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The Correct Option is D

Solution and Explanation

Step 1: Note what the circumferences really tell us.
Flow through a pipe depends on its cross section area, and area scales with the square of the circumference, so inlet area : outlet area = \(15^2:10^2 = 225:100 = 9:4\).
This means whatever the outlet's own time to empty the tank is, the inlet's time is automatically fixed by this same 9:4 rate ratio, and vice versa.

Step 2: Statement 1 path.
Outlet empties the tank in 25 minutes, so its rate is \(1/25\) tank/minute.
Inlet rate = outlet rate x \(9/4\) = \(9/100\) tank/minute.
Net rate with both open = \(9/100 - 4/100 = 1/20\) tank/minute, so the tank fills in exactly 20 minutes. A single number comes out, so statement 1 alone works.

Step 3: Statement 2 path.
Inlet fills the tank in 56 minutes, so its rate is \(1/56\) tank/minute.
Outlet rate = inlet rate x \(4/9\) = \(1/126\) tank/minute.
Net rate with both open = \(1/56 - 1/126\), again a single fixed value, giving one specific filling time. So statement 2 alone works too, even though its number differs from statement 1's (each statement is a separate, self-contained scenario).

Step 4: Conclude.
Since the stem's circumference ratio always supplies the missing rate link, either statement used on its own is enough to compute a filling time. \[ \boxed{\text{d}} \]
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