Subject: General Aptitude · Chapter: Square Roots and Cube Roots · Exam: 2005 · Marks: · Difficulty:
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.
(a)32
(b)34
(c)35
(d)36
Answer
Answer (as printed): D
Explanation
Let the total number of camels be $x$. Then, $x-\left(\frac{x}{4}+2 \sqrt{x}\right)=15 \Leftrightarrow \frac{3 x}{4}-2 \sqrt{x}=15$ $$\begin{aligned} & \Leftrightarrow 3 x-8 \sqrt{x}=60 \Leftrightarrow 8 \sqrt{x}=3 x-60 \\ & \Leftrightarrow 64 x=(3 x-60)^{2} \Leftrightarrow 64 x=9 x^{2}+3600-360 x \\ & \Leftrightarrow 9 x^{2}-424 x+3600=0 \Leftrightarrow 9 x^{2}-324 x-100 x+3600=0 \\ & \Leftrightarrow 9 x(x-36)-100(x-36)=0 \Leftrightarrow(x-36)(9 x-100)=0 \\ & \Leftrightarrow x=36 . \\ & {\left[\because x \neq \frac{100}{9}\right]} \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.