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Question

Tap P can fill a tank in 2hours while Tap Q can fill the same tank in 3hrs. Tap R can empty the same tank in 6hrs. All the taps are turned on at the same time.

(a) How long does it take to fill the tank completely?

(b) How long will it take to fill 3/4 of the tank?

 

Thanks!

Answer

(a)
In 1 h,
Tap P fills 1/2
Tap Q fills 1/3
Tap R empties 1/6
All 3 taps ——-> (1/2) + (1/3) – (1/6) = 2/3
2/3 ——-> 1 h
1/3 ——-> 1/2 h
3/3 ——-> 3/2 h = 1 1/2 h

(b)
3/4 ——-> (3/2) x (3/4) = 9/8 = 1 1/8 h

Ans : (a) 1 1/2 h; (b) 1 1/8 h.

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Let x be volume of tank

Rate of flow of tap P = x/2

Rate of flow of tap Q = x/3

Rate of flow of tap R = x/6

a) To find how long it takes to fill tank, first find rate of water into tank after all taps turned on

Rate = x/2 + x/3 – x/6 = 2x/3

Time = x /(2x/3) = 3/2 hrs

b) Time = (3x/4) / (2x/3) =9/8 hrs

 

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