(d) 36
Suppose the total number of cows = x
\(\frac14x\) of the cows are in the forest.
\(2\sqrt{x}\) have gone to mountains.
15 are on the banks of a river.
∴ \(2\sqrt{x}\) + \(\frac14x\) + 15 = x
⇒ \(2\sqrt{x}\) - \(\frac34x\) + 15 = 0
⇒ \(8\sqrt{x}\) - 3x + 60 = 0
⇒ 3y2 - 8y - 60 = 0 (Let √x = y)
⇒3y2 - 18y + 10y -60 = 0
⇒ 3y(y - 6) + 10(y - 6) = 0
⇒ (3y +10)(y -6) = 0 ⇒ y = \(\frac{10}{3}, 6\)
⇒ \(\sqrt{x}\) = y = 6 (Rejecting –ve value)
⇒ x = 36.