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 :

Options

A. 6
B. 100
C. 63
D. 36

Answer

D

Explanation

Let the number of cows = x
Then, according to the question, `2sqrt(x) + 1/4 x + 15 =x`
or `2sqrt(x) - 3/4x + 15 = 0`
or`8sqrt(x) - 3x + 60 = 0`
or `3x - 8sqrt(x) - 60 = 0`
or `3(sqrt(x))^2 - 18sqrt(x) + 10sqrt(x) -60 = 0`
or, `3sqrt(x) (sqrt(x) - 6) + 10(sqrt(x) - 6) = 0`
or , `(sqrt(x) - 6)(3sqrt(x) + 10) = 0`
or `x = 36` and `x = 100/9`
But ,`x = 100/9` is discarded.
[`because` No. of cows can.t be in fraction ]
So, `x = 36`
Therefore, the number of cows = `x= 36`.