Question

Out of group of Swans, $\frac{7}{2}$ times the square root of number of Swans are playing on the shore of the tank. Remaining two are quarreling in the water. Calculate the total number of Swans. Find the number of Swans playing on the shore of the tank.

• A. $14,16$
• B. $16,12$
• C. $14,12$
• D. $16,14$

Answer 1

The correct option is D $16,14$

Let $x$ be the total no. of Swans.

$\therefore$ No. of swans playing $=\frac{7}{2}\sqrt{x}$

$\because$ remaining $2$ are quarrelling in the water

$⟹\frac{7}{2}\sqrt{x}+2=x$

$⟹x-\frac{7}{2}\sqrt{x}-2=0$

$⟹(\sqrt{x}{)}^2-2\times \frac{7}{2\times 2}\sqrt{x}+\frac{49}{16}-\frac{49}{16}-2=0$

$⟹(\sqrt{x}{)}^2-2\times \frac{7}{4}\times \sqrt{x}+{\left(\frac{7}{4}\right)}^2-\frac{81}{16}=0$

$⟹{(\sqrt{x}-\frac{7}{4})}^2-{\left(\frac{9}{4}\right)}^2=0$

$⟹(\sqrt{x}-\frac{7}{4}+\frac{9}{4})(\sqrt{x}-\frac{7}{4}-\frac{9}{4})=0$

$⟹(\sqrt{x}-\frac{7}{4}+\frac{9}{4})=0$ or $(\sqrt{x}-\frac{7}{4}-\frac{9}{4})=0$

$⟹\sqrt{x}=\frac{1}{2}$ or $\sqrt{x}=4$

$⟹$ $x=16$.

Thus, no. of swans playing $=\frac{7}{2}\times 4=14$

Hence, total no. of swans is $16$ and playing swans are $14$.