One-fourth of a herd of cows is in the forest. Twice the square root o

1.	One-fourth of a herd of cows is in the forest. Twice the square root of the herd has gone to mountains and the remaining 15 are on the banks of a river. The total number of cows is : (a) 6 (b) 100 (c) 63 (d) 36
Answer» (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.

One-fourth of a herd of cows is in the forest. Twice the square root of the herd has gone to mountains and the remaining 15 are on the banks of a river. The total number of cows is : (a) 6 (b) 100 (c) 63 (d) 36

Answer»

(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.