Question

43. A cistern is normally filled in 6 h but takes 4 h longer
to fill because of a leak in its bottom. If the cistern
is full, the leak will empty it in how much time?
(a) 15 h
(b) 16 h
(c) 20 h
(d) None of these

Answer 1

Answer:

Step-by-step explanation:

Let’s try and solve it with minimum calculations.

Cistern is filled completely in 6 hours. So let the cistern is of 60L, So the pipe fills at rate of 10L per hour.

Due to the leak, it takes 10 hours fill. So, the rate is reduced to 6L per hour.

This means the leak empties at a rate of 4L per hour(10Lph - 6Lph)

So to empty the entire tank, it would take 60/4 = 15 hours.

Alternate Way:

Due to the leak the pipe is working for extra 4 hours. Or we can say the pipe is doing extra 2/3rd of the total work in 10 hours (2/3rd of 6 hours is 4 hours) .

So the leak empties 2/3rd of the tank in 10 hours. So to empty the total tank, it will take 15 hours!