Question

Two taps A and B can fill an oil tank in 15 min and 18
min respectively while a third tap is used to empty
the tank. The third tap is opened after 6 min of
1
opening of tap A and B. If the tank empties in 16
2.
min after opening the third tap then in how much
time the third tap can empty the full tank?​

Answer 1

Given :- Two taps A and B can fill an oil tank in 15 min and 18 min respectively while a third tap is used to empty the tank. The third tap is opened after 6 min ofopening of tap A and B. If the tank empties in 16 min after opening the third tap then in how muchbtime the third tap can empty the full tank ?

Solution :-

→ LCM of 15 and 18 = 90 Litre = Let capacity of oil Tank .

so,

→ Efficiency of Tap A = Capacity / Time = 90 / 15 = 6 litre / min.

and,

→ Efficiency of Tap A = Capacity / Time = 90 / 18 = 5 litre / min.

now, Let us assume that, the Efficiency of Tap C empties the tank is x litre / min.

then,

→ 6(A + B) - 16(A + B - C) = 0 (as tank was empties.)

→ 6(A + B) = 16(A + B - C)

putting efficiency of all three,

→ 6(6 + 5) = 16(6 + 5 - x)

→ 6 * 11 = 16(11 - x)

→ 33 = 88 - 8x

→ 8x = 88 - 33

→ 8x = 55

→ x = (55/8) Litre / Min.

therefore,

→ Time taken by tap C to empty the full tank = Capacity / Efficiency = 90 / (55/8) = (90 * 8) / 55 = (18 * 8)/11 = (144/11) = 13(1/11) Minutes. (Ans.)

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Answer 2

Step-by-step explanation:

Answer will be 6 minute if there are 16.5 minute