Three taps A, B, and C can fill a tank in 10, 15, and 30 hours respectively. If all three taps are opened together, in how many hours will the tank be filled?
Combined rate = 1/10 + 1/15 + 1/30 = (3 + 2 + 1)/30 = 6/30 = 1/5 tank per hour. Time = 5 hours.
A and B can do a piece of work in 12 days and 16 days respectively. They worked together for 4 days, and then A left. How many more days will B take to finish the remaining work?
In 4 days together: 4*(1/12 + 1/16) = 4*(7/48) = 7/12 work done. Remaining work = 5/12. B's time = (5/12) / (1/16) = 80/12 = 6.67 days.
If 10 men or 15 women can harvest a field in 20 days, how many days will 6 men and 6 women take to harvest the same field?
10 M = 15 W => 1 $M = 1.5 W$. 6 M + 6 $W = 6(1.5) + 6 = 15 W$. 15 W harvest in 20 days.
Which of the following statements are CORRECT about A, B, and C completing work in 6, 8, and 12 days?
The listed statements are correct.
A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills water at the rate of 6 liters per minute. When the tank is full, the inlet is opened and due to the leak the tank is emptied in 12 hours. Find the capacity of the tank in liters.
Rate of leak = 1/8. Net rate = 1/12. Inlet rate = 1/8 - 1/12 = 1/24 tank per hour. Inlet fills full tank in 24 hours. Rate = 6 L/min = 360 L/hour. Capacity = 24 * 360 = 8640 liters.