One-fourth of a herd of cows is in the forest. Twice the square root of the herd has gone to mountains and he remaining $15$ are on the banks of a river. The total number of cows is:

6

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100

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63

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36

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Solution

The correct option is D $36$
Let the total number of cows be x.
Hence
$\frac{x}{4} + 2 \sqrt{x} + 15 = x$
$\frac{3 x}{4} - 15 = 2 \sqrt{x}$
$3 x - 60 = 8 \sqrt{x}$
Let $\sqrt{x} = y$
$∴ 3 y^{2} - 8 y - 60 = 0$
$y = 6$ and $y = \frac{- 10}{3}$
$∴ \sqrt{x} = 6$
$x = 36$

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One-fourth of a herd of cows is in the forest. Twice the square root of the herd has gone to mountains and he remaining 15 are on the banks of a river. The total number of cows is:

The correct option is D 36Let the total number of cows be x.Hencex4+2√x+15=x3x4−15=2√x3x−60=8√xLet √x=y∴3y2−8y−60=0y=6 and y=−103∴√x=6x=36

One-fourth of a herd of cows is in the forest. Twice the square root of the herd has gone to mountains and he remaining $15$ are on the banks of a river. The total number of cows is:

The correct option is D $36$
Let the total number of cows be x.
Hence
$\frac{x}{4} + 2 \sqrt{x} + 15 = x$
$\frac{3 x}{4} - 15 = 2 \sqrt{x}$
$3 x - 60 = 8 \sqrt{x}$
Let $\sqrt{x} = y$
$∴ 3 y^{2} - 8 y - 60 = 0$
$y = 6$ and $y = \frac{- 10}{3}$
$∴ \sqrt{x} = 6$
$x = 36$