One-fourth of a herd of camels was seen in the forest. Twice the square root of

Question

One-fourth of a herd of camels was seen in the forest. Twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Find the total number of camels ?

Options:

A . 32

B . 34

C . 35

D . 36

Answer: Option D
Let the total number of camels be x
Then,
$$\eqalign{
& \Leftrightarrow x - \left( {\frac{x}{4} + 2\sqrt x } \right) = 15 \cr
& \Leftrightarrow \frac{{3x}}{4} - 2\sqrt x = 15 \cr
& \Leftrightarrow 3x - 8\sqrt x = 60 \cr
& \Leftrightarrow 8\sqrt x = 3x - 60 \cr
& \Leftrightarrow 64x = {\left( {3x - 60} \right)^2} \cr
& \Leftrightarrow 64x = 9{x^2} + 3600 - 360x \cr
& \Leftrightarrow 9{x^2} - 424x + 3600 = 0 \cr
& \Leftrightarrow 9{x^2} - 324x - 100x + 3600 = 0 \cr
& \Leftrightarrow 9x\left( {x - 36} \right) - 100\left( {x - 36} \right) = 0 \cr
& \Leftrightarrow \left( {x - 36} \right)\left( {9x - 100} \right) = 0 \cr
& \Leftrightarrow x = 36\,\,\,\,\,\,\,\,\,\,\,\,\left[ {\because x \ne \frac{{100}}{9}} \right] \cr} $$

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