Multiple choice

Directions: The question given below is followed by two statements labelled I and II. You have to determine whether the data given in the statements is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. How long will leakage take to empty the full tank? (I) Pipe A takes 2 hours to fill half the tank and takes 1 extra hour, if there is a leakage. (II) The cistern has a capacity of 240 litres. Pipe A takes 5 hours to fill the whole tank, if there is a leakage.

  1. The question can be answered by using statement-I alone, but cannot be answered using the other statement alone.

  2. The question can be answered by using statement-II alone, but cannot be answered using the other statement alone.

  3. The question can be answered by using either of the statements alone.

  4. The question can be answered using both the statements together, but cannot be answered using either of the statements alone.

  5. The question cannot be answered even by using both the statements together.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I says Pipe A fills half in 2 hours (full in 4 hours). With leakage, it takes 1 extra hour (5 hours total). Let L be the time for the leak to empty the tank. 1/4 - 1/L = 1/5. This allows solving for L. Statement II provides similar info but is redundant or consistent. Thus, I alone is sufficient.

AI explanation

Using statement I, pipe A takes 2 hours to fill half the tank, meaning its normal filling time is 4 hours; with the leakage, it takes 1 extra hour to fill this half, so its rate is 1/10 per hour. Since the net rate of 1/10 equals the normal rate of 1/4 minus the leak rate, the leak empties the tank at 3/20 per hour, taking 20/3 hours. Statement II provides the total capacity of 240 litres and states pipe A takes 5 hours with a leak, but without knowing either the normal filling time of pipe A or the water discharge per hour, the leak rate cannot be determined; thus, only statement I is sufficient.

Keep practicing — related questions