Question

A tank is fitted with two taps A and b: In how much time will the tank be full if both the taps are opened together?
I. A is 50% more efficient than B
II. A alone takes 16 hours to fill the tank
III. B alone takes 24 hours to fill the tank

• A. I and III only
• B. Any two options will suffice
• C. I and II only
• D. II and III only

Answer 1

The Correct Option is B

To determine how much time it will take to fill the tank when both taps A and B are opened together, we analyze the information given:

Let's denote the rate of tap A as R_A, and the rate of tap B as R_B. The efficiency and time taken by each tap relates directly to its filling rate.

• From statement I: A is 50% more efficient than B. This means R_A = 1.5 × R_B.
• From statement II: A alone takes 16 hours. Therefore, R_A = 1/16 of the tank per hour.
• From statement III: B alone takes 24 hours. Hence, R_B = 1/24 of the tank per hour.

We will now analyze the information from both pairs of statements given:

• Using II and III: Knowing the individual rates R_A = 1/16 and R_B = 1/24, we can find the combined rate when both taps are open simultaneously
• Combined rate, R_Total = R_A + R_B = (1/16 + 1/24). To simplify, find the common denominator, which is 48.

RTotal	= 3/48 + 2/48
	= 5/48 (tank per hour)
Total time to fill the tank	= 1/RTotal
	= 48/5
	= 9.6 hours

• Using I and II: Since A is 50% more efficient than B, convert this into a rate relationship: if R_B = x, then R_A = 1.5x. We know R_A from II: 1/16 = 1.5x, solving gives x = 1/24, which is consistent with III for R_B.

Similarly, using I and III will lead us to the same rates. This confirms the given answer: "Any two options will suffice" because any pair of statements will indeed provide enough information to deduce the filling time when both taps A and B are used simultaneously.