Question

A tank is filled completely in 2 hours if boththe taps are open. If only one of the taps is open at the given time,the smaller tap takes 3 hours more than the larger one to fill the tank. How much time does each tap take to fill thetank completely

Answer 1

Let larger tap can fills the tank in = x hrs.

then smaller tap will fill the tank in = (x+3) hrs

Part of the tank filled in an hr by both taps =1/x+1/(x+3) acordingly:-

1/x + 1/(x+3) = 1/2

(x+3+x)/x.(x+3) =1/2

or (2x+3)/(x^2+3x) = 1/2

or x^2+3x = 4x+6

or x^2 - x - 6 = 0

or (x-3) (x+2) = 0

x= 3 , -2(Negligenle )

Larger tap can fills the tank in = x hrs = 3 hrs.

Smaller tap can fills in = (x+3 )=(3+3)= 6 hrs.