TIPS on cracking Aptitude Questions on Time and Work

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Assume that the productivity of each worker is constant

1.    Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs.3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

Solution:

Let the total amount of work to be done be W units.

Productivity of A, Pa = W/6 units per day.

Productivity of B, Pb = W/8 units per day.

3 days x [Pa + Pb + Pc] = W => Pc = W/24 units per day

Ratio of wages of A: B: C = Ratios of their productivities = (W/6): (W/8): (W/24) = 4: 3: 1.

Amount to be paid to C = Rs.3200 x (1/8) = Rs.400

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2.    Question: It takes 6 hours for pump A, used alone, to fill a tank of water. Pump B used alone takes 8 hours to fill the same tank. We want to use three pumps: A, B and another pump C to fill the tank in 2 hours. What should be the rate of pump C? How long would it take pump C, used alone, to fill the tank?

Solution:

Let the total capacity of the tank be C liters.

Fill rate of pump A, Fa = C/6 liters per hr

Fill rate of pump B, Fb = C/8 liters per hr

2 hrs x [Fa + Fb + Fc] = C => Fc = 5C/24 liters per hr

Let‘t’ be the time taken by only pump C to fill the tank.

‘t’ hrs x 5C/24 = C => t = 24/5 = 4.8 hrs

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