Question

There are 3 pipes in our tank. with these 3 pipes separately the tank can be filled up in 18,
21 & 24 hours respectively. (a) If the 3 pipes remain open together let's make proportion
and calculate when the tank will be filled with water. (b) If the first two pipes would remain
open,
let's calculate the time to fill up the tank with water. (c) If the last two pipes would
remain open, let's calculate the time to fill up the tank.
​

Answer 1

Answer:

(a) 6.904 hours

(b) 9.692 hours

(c) 11.2 hours

Step-by-step explanation:

Let's assume volume of the tank is V.

Pipe 1 fill this tank in 18 hours.

so in 1 hour tank filled by Pipe 1 = V/18

same procedure we will do for Pipe 2 and Pipe 3.

In 1 hour tank filled by Pipe 2 = V/21

In 1 hour tank filled by Pipe 3 = V/24

(a) When all three Pipes are filling tank

Tank filled by three Pipes in 1 hour = V/18 + V/21 + V/24

Tank filled = 73V/504

It will take 504/73 or 6.904 hours to fill the tank by three Pipes.

(b) When first two pipes are filling tank.

Tank filled by first two Pipe in 1 hour = V/18 + V/21

Tank filled = 13V/126

So, It will take 126/13 or 9.692 hours to fill the tank by first two Pipes.

(c) When last two Pipes are filling tank

Tank filled by last two pipe in 1 hour = V/21 + V/24

Tank filled = 45V/504

So, It will take 504/45 or 11.2 hours to fill the tank by last two pipes.

Answer 2

Answer:

1st pipe fills in 18 hours , therefore in 1 hour it fills 1/18 th of a tank

2nd pipe fills in 21 hours, therefore in 1 hour it fills 1/21 th of a tank

3rd pipe fills in 24 hours, therefore in 1 hour, it fills 1/24 th of a tank.

(case 1), when all the pipes are open simultaneously, they together will fill

1/18+1/21+1/24 = (28+24+21)/504

=> 73/504 th level of the tank

therefore together they will take 504/73

=> 6.9 hours to fill the tank

(case 2) if first two taps are opened, they together will fill 1/18+1/21 = (7+6)/126 = 13/126 th of a tank

therefore together they will take 126/13

=> 9.7 hours to fill the tank

(case 3) if the last two pipes are opened, they together will fill 1/21+1/24 = (8+7)/168 = 15/168 th of a tank

therefore together they will take 168/15

=> 11.2 hours to fill the tank