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In a tank there are three inlet pipes. The first two pipes fill the tank in 10 minutes. Second and third pipe can fill the tank in 15 minutes. Also it can be filled through the first and the third inlet pipes in 20 minutes. How much time is required to fill up the tank by all the three inlet pipes?

In a tank there are three inlet pipes. The first two pipes fill the tank in 10 minutes. Second and third pipe can fill the tank in 15 minutes. Also it can be filled through the first and the third inlet pipes in 20 minutes. How much time is required to fill up the tank by all the three inlet pipes? Correct Answer 120/13 minutes

Given:

First two pipes fill the tank = 10 minutes

Second and third can fill the tank = 15 minutes

First and third filled = 20 minutes

Calculation:

Let the first, second and third pipe be P, Q and R

P and Q fill the tank in 1 hour = 1/10

1/P + 1/Q = 1/10     ----(i)

Q and R fill the tank in 1 hour = 1/25

1/Q + 1/R = 1/15     ----(ii)

P and R fill the tank in 1 hour = 1 / 40

1/P + 1/R = 1/20     ----(iii)

equation (i) - (ii)

⇒ 1/P – 1/R = 1/10 – 1/15

⇒ 1/P – 1/R = (3 – 2)/ 30

⇒ 1/P – 1/R = 1/30     ----(iv)

From equation (iii) and (iv)

⇒ 2/P = (1/20) + (1/30)

⇒ 2/P = (3 + 2)/60

⇒ 2/P = 5/60

⇒ 2/P = 1/12

⇒ P = 24

P = 24 putting in equation ( 3 )

⇒ 1/24 + 1/R = 1/20

⇒ 1/R = 1/20 – 1/24

⇒ (6 – 5)/120

⇒ 1/R = 1/120

⇒ R = 120

Let the time taken to full the tank be x

x (1/P + 1/Q + 1/R) = 1

⇒ x (1/24 + 1/15) = 1

⇒ x = 1

⇒ x (13/120) = 1

⇒ x = 120/13 minutes

∴ Time taken by all three pipes to fill the complete tank is 120/13 minutes.

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