Multiple choice

Three pipes A, B and C can fill a tank in 5 hours. After working at it together for 3 hours, C is closed and A and B can fill the remaining part in 6 hours. The number of hours taken by C alone to fill the tank is

  1. 10.5 hours

  2. 12 hours

  3. 8 hours

  4. 7.5 hours

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the total work be 1 unit. Combined rate of A+B+C = 1/5. In 3 hours, they complete 3/5 of the work. Remaining work = 2/5. A and B complete this in 6 hours, so their combined rate (A+B) = (2/5) / 6 = 1/15. Rate of C = (A+B+C) - (A+B) = 1/5 - 1/15 = 2/15. Time for C = 1 / (2/15) = 7.5 hours.

AI explanation

Using the LCM method, assume the total capacity of the tank is 15 units, so the combined rate of A, B, and C is 3 units per hour. In 3 hours, they fill 9 units, leaving 6 units to be filled by A and B in 6 hours, giving A and B a combined rate of 1 unit per hour. The rate of C alone is 2 units per hour (3 minus 1). Therefore, C alone takes 7.5 hours to fill the tank.

Keep practicing — related questions