Time taken by pipe P and Q to fill up the tank is 60/ 7 minutes and time taken to fill the whole tank when all three pipes are open is 300/ 23 minutes. Ratio of time taken by pipe P to fill up the tank and pipe Q is 3 : 4. Calculate time taken by Q and R to fill up the tank. (Pipe R is a drain pipe.)?

Question

Time taken by pipe P and Q to fill up the tank is 60/ 7 minutes and time taken to fill the whole tank when all three pipes are open is 300/ 23 minutes. Ratio of time taken by pipe P to fill up the tank and pipe Q is 3 : 4. Calculate time taken by Q and R to fill up the tank. (Pipe R is a drain pipe.)?

10 minutes
95/7 minutes
100 minutes
105/7 minutes
110/3 minutes

LohaHridoy

14 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 3 : 100 minutes

Given:

Pipe P + Pipe Q = 60/7 minutes

Pipe P + Pipe Q - Pipe R = 300/23 minutes

Pipe P : Pipe Q = 3 : 4

Formula:

If time taken by pipe A to fill tank is ‘a’ minutes and by pipe B is ‘b’ minutes then total time taken to fill the tank t ⇒ (1/t) = (1/a) + (1/b)

Calculation:

Let, time taken by pipe P be X

⇒ Time taken by pipe Q = 4 × X/ 3

⇒ 7/ 60 = (1/ X) + (3/(4X))

⇒ 7/ 60 = (4 + 3)/4X

⇒ 7/ 60 = 7/4X

⇒ 60 = 4X

⇒ X = 15

⇒ Time taken by pipe Q = 20 (∵ 4 × 15/3 = 20)

Let, time taken by pipe R be Y

⇒ 23/ 300 = (7/ 60) - (1/Y)

⇒ 1/ Y = (7/ 60) + (23/300)

⇒ 1/ Y = (35 – 23)/300

⇒ Y = 25 (∵ 300/12 = 25)

Now finding time taken by Q and R to fill the tank

⇒ 1/ t = (1/ 20) - (1/25)

⇒ 1/ t = (25 - 20)/500

⇒ 1/ t = 1/100

⇒ t = 100/1 minutes

∴ it takes 100 minutes to fill the tank

Confusion PointsTime taken by two pipe to fill a tank is 60/ 7 = 8.57 min (approx.)

Time taken by three pipe to fill a tank is 300/ 23 = 13 min (approx.)

As three pipe together takes more time than two pipes.

That means the one pipe drain pipe taking water out of tank.

Hence, R time is been subtracted.