Question

A cistern can be filled separately by two pipes P and Q in 45 minutes and 35 minutes respectively. A tap R at the bottom can empty the full cistern in 30 minutes. If the tap R is opened 7 minutes after the two pipes P and Q are opened then after what time from the opening of tap R the cistern becomes full?​

Answer 1

I am not getting the answer

Answer 2

Given :-

• P pipe alone can fill the cistern in = 45 Min.
• Q pipe alone can fill the cistern in = 35 Min.
• R Tap alone can Empty the full cistern in = 30 Min.
• The tap R is opened 7 minutes after the two pipes P and Q are opened.

To Find :-

• After what time from the opening of tap R the cistern becomes full ?

Solution :-

→ LCM of 45,35 and 30 = 630 Litre = Let Capacity of cistern.

Than,

→ Efficiency of Pipe P = Capacity of cistern / (Time Taken) = 630 / 45 = 14 Litre/Min.

→ Efficiency of Pipe Q = Capacity of cistern / (Time Taken) = 630 / 35 = 18 Litre/Min.

→ Efficiency of Tap R = Capacity of cistern / (Time Taken) = 630 / 30 = 21 Litre/Min. { out. }

Now, for the first 7 Minutes Both (P + Q) were opened .

So,

→ In 1 minute (P + Q) Fill = (14 + 18) = 32 litre (inside)

→ in 7 Minutes (P+Q) Filled = 32 * 7 = 224 Litre .(inside).

Than,

→ Left to be filled in cistern = 630 - 224 = 406 Litre.

__________

Now, Tap R is Also Opened .

→ (P + Q) Fill in one minute = (14 + 18) = 32 Litre inside

→ R Empty in one minute = 21 Litre .

So,

→ water going inside in One Minute = 32 - 21 = 9 Litre.

__________

Therefore,

→ Time taken to fill the Remaining Empty cistern = (Left to be filled) / (Efficiency of all three)

→ Required Time = (406/9) = 45(1/9) Minutes. (Ans.)

Hence, from the opening of tap R the cistern becomes full in 45(1/9) Minutes..