Water is pouring into a tank at a constant rate. when the tank is full, 10 pumps of equal capacity empty the tank in 12 hrs, while 15 pumps of the same capacity empty the tank in 6 hrs. The time which 25 pumps of the same capacity take to empty the tank, if the tank in initially full, will be :

Explanation

Let each pump can fill a tank in x hrs and each pump can empty the tank in y hrs.
`therefore` Each pump can fill in 1 hr = `(1)/(x)` tank
Each pump can empty in 1 hr = `(1)/(y)` tank
So, according to the given problem,
`(10)/(y) - (1)/(x) = (1)/(12) " ...(1)"`
and `(15)/(y) - (1)/(x) = (1)/(6) " ...(2)"`
Subtracting equation (1) from equation (2),
`(5)/(y) = (1)/(6) - (1)/(12) implies (5)/(y) = (1)/(12) implies y = 60`
Putting y = 60 in equation (1), we get
`(10)/(60) - (1)/(x) = (1)/(12) implies (1)/(x) = (1)/(6) - (1)/(12) = (1)/(12) `
`therefore x = 12`
If there are 25 pumps, then in 1 hr, they will empty = `(25)/(60) - (1)/(12) = (1)/(3)` tank.
Hence, the entire tank will be empty in 3 hrs.