Question

A cylindrical overhead container is filled by two pumps P1 and P2. P1 can fill the container in 8 hr while P2
can fill the container in 12 hr. There is a pipe P3 which can empty the container in 8 hr. Both the pumps are
opened simultaneously. The supervisor of the container, before going out for some work sets a timer to
open P3 when the container is half filled so that the container is exactly filled up by the time he is back. Due
to technical fault P3 opens when the container is one-third fil

0.15

0.12

0.1

None of these​

Answer 1

Complete Question :- A cylindrical overhead container is filled by two pumps P1 and P2. P1 can fill the container in 8 hr while P2 can fill the container in 12 hr. There is a pipe P3 which can empty the container in 8 hr. Both the pumps are opened simultaneously. The supervisor of the container, before going out for some work sets a timer to open P3 when the container is half filled so that the container is exactly filled up by the time he is back. Due to technical fault P3 opens when the container is one-third filled . If the supervisor comes back as per the plan what percent of the tank is till empty ?

Answer :-

→ LCM of 8 and 12 = 24 litre = Let Capacity of tank .

so,

→ Efficiency of P1 = Capacity / Time taken = 24/8 = 3 litre/hour.

→ Efficiency of P2 = Capacity / Time taken = 24/12 = 2 litre/hour.

→ Efficiency of P3(empty) = Capacity / Time taken = 24/8 = (-3) litre/hour.

now,

→ Half filled by (P1 + P2) in = 12/(3+2) = (12/5) hours.

then,

→ Rest half filled by (P1 + P2 - P3) in = 12/(3 + 2 - 3) = 6 hours.

so,

→ Total time taken to fill the tank = (12/5) + 6 = (42/5) hours = Time in which the supervisor comes back .

now, due to technical error :-

→ (1/3) filled by (P1 + P2) in = (1/3) of 24 = 8 litre = (8/5) hours .

now,

→ Time left for (p1 + p2 - p3) = (42/5) - (8/5) = (34/5) hours.

so,

→ in (34/5) hours (p1 + p2 - p3) fills = (34/5) * (3 + 2 - 3) = (68/5) litre .

then,

→ Total water in the tank is = 8 + (68/5) = (108/5) litre .

therefore,

→ Tank is still empty = 24 - (108/5) = (12/5) litre .

hence,

→ Required % = {(12/5) * 100} / 24 = (12 * 20)/24 = 10% (Ans.)

{Excellent Question.}

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