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A, B and C are 3 small pumps fitted to a tank. D is a large pump fitted to the tank. B is 50% more efficient than A. C is 33.33% more efficient than B. D is 50% more efficient than C. All of the pumps are used to fill the tank. Find the ratio of the time taken by all the pumps to fill the tank when pump D is used to empty the tank and other are used to fill the tank to the time taken when all are used to fill the tank?

A, B and C are 3 small pumps fitted to a tank. D is a large pump fitted to the tank. B is 50% more efficient than A. C is 33.33% more efficient than B. D is 50% more efficient than C. All of the pumps are used to fill the tank. Find the ratio of the time taken by all the pumps to fill the tank when pump D is used to empty the tank and other are used to fill the tank to the time taken when all are used to fill the tank? Correct Answer <span style=" line-height: 107%; ">5 : 1</span>

CALCULATION: 

Suppose A fills 2x litres a day.

Given, B is 50% more efficient than A.

∴ B fills 3x litres a day.

⇒ C fills (4/3) × (3x) = 4x litres a day.

⇒ D fills 6 litres a day.

If D starts emptying, then

D empties (3/2) × 4x = 6x litres a day.

The L.C.M. of (2x, 3x, 4x and 6x) is 12x.

Let the total capacity of the tank be 12x litres.

Case (I): 

Time taken by all the pumps to fill the tank together when pump D fills = 12x/(15x) = (4/5) days

Case (II): 

Time taken by all the pumps to fill the tank together when pump D empties = 12x/(2x + 3x + 4x - 6x) = 12x/3x = 4 days

∴ Required ratio = 4 : 4/5 = 5 : 1

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