3 Two pipes A and B can fill a tank in 3 7 hours when opened simultaneously. If B alone can take 2 hours less than A alone takes to fill the tank completely. How much time does A alone take to fill the tank?

Explanation

Let us assume that A alone takes 'x' hours to fill the tank. B alone takes 'x - 2' hours to fill the tank. 1 Part of the tank filled by pipe A in 1 hour = x 1 Part of the tank filled by pipe B in 1 hour = x−2 3 24 Together they fill the tank in 37 hr = 7 hr 24 1 1 7 ( x + x−2 ) = 1 On simplifying, we get 24(2x − 2) = 7x(x − 2) 7x2 − 62x + 48 = 0 6 (x − 8)(x − 7 ) = 0 6 ∴ x = 8 ( x can't take the value of 7 as x − 2 is negative ) Hence, A alone takes 8 hr to fill the tank completely.