Question

For irrigational purposes, a farmer uses a tank of water. He uses a pipe during night to fill the tank, so that he could use the tank of water in the morning to irrigate his farm. The pipe fills the tank in 3 hours but on one particular day, because of a leak in the tank, the pipe takes 4.5 hours to fill it. In how many hours can the tank be completely emptied by the leak alone?
​

Answer 1

Step-by-step explanation:

From Rabindranath Tagore in 1913 to Abhijit Vinayak Banerjee in 2020, there are 10 Indian Nobel prize winners so far who have made the country feel proud. Abhijit Banerjee has won the Nobel prize for his outstanding work in economics last year

Answer 2

Answer:

it takes 9 hours to completely empty the tank due to leak alone

Step-by-step explanation:

given, time taken to fill the tank = 3 hours

so in 1 hour, it fills $\frac{1}{3}$ of the tank

due, to leak, it took 4.5 hours to fill the tank

let x be the time taken to empty the tank due to the leak

then, in 1 hour, $\frac{1}{x}$ part of the tank is emptied

to find the total time taken to empty the tank,

$\frac{1}{3} - \frac{1}{x} = \frac{1}{4.5}$

⇒ 4.5 (x-3) = 3x

⇒4.5x - 13.5 = 3x

⇒1.5x = 13.5

⇒ x = $\frac{13.5}{1.5}$

⇒ x= 9

therefore, it takes 9 hours to completely empty the tank due to leak alone