Multiple choice

The efficiency of inlet pipe P is 20% more than that of the inlet pipe Q so the pipe P takes 24 minutes less to fill a water tank of capacity 6000 litres. Quantity I : How much time, the pipe P and the pipe Q together will take to fill a water tank of capacity 8800 litres? Quantity II : 99 minutes

  1. Quantity : I > Quantity : II

  2. Quantity : I ≥ Quantity : II

  3. Quantity : I < Quantity : II

  4. Quantity : II ≥ Quantity : I

  5. Quantity I = Quantity II or relation can't be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let efficiency of Q be x, P be 1.2x. Time taken by P = 6000/1.2x = 5000/x. Time taken by Q = 6000/x. Difference = 1000/x = 24 mins. x = 1000/24 = 125/3. Time for P and Q together for 8800L = 8800 / (x + 1.2x) = 8800 / 2.2x = 4000 / x = 4000 / (125/3) = 4000 * 3 / 125 = 32 * 3 = 96 minutes. Since 96 < 99, Quantity I < Quantity II.

AI explanation

If the efficiency of pipe P is 20% more than pipe Q, their efficiency ratio is 6:5, making their time ratio 5:6. Since the difference of 24 minutes represents 1 ratio unit, pipe P takes 120 minutes and pipe Q takes 144 minutes to fill the 6000 litre tank, meaning their rates are 50 litres per minute and 41.66 litres per minute respectively. Their combined rate is 91.66 litres per minute, calculated as (6000/120) plus (6000/144). The time taken by both pipes to fill an 8800 litre tank is 8800 divided by 91.66, which equals 96 minutes. Quantity I is 96 minutes and Quantity II is 99 minutes, so Quantity I is less than Quantity II.

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