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Q.

Out of a group of swans $\frac{7}{2}$ times the square root of the total number are playing on the shore of a pond. The two remaining ones are swimming in water. Find the total number of swans.

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a

16

b

17

c

18

d

19

answer is A.

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Detailed Solution

Given that out of a group of swans,

\frac{7}{2}

times the square root of the total number are playing on the shore of a tank, the two remaining ones are swimming in the water.
Quadratic equation is expressed as

a x 2 + b x + c = 0

where x is the unknown variable and a,b,c are the coefficients.
Let us find the total no of swans.
Suppose the total number of swans be x and swans playing on the shore be

\frac{7}{2} \sqrt{x .}

Since the two remaining ones are swimming in the water, the total no. of swans is

x = 72 x + 2 ⇒ x − 2 = 72 x ⇒ x − 2 2 = 72 x 2 ⇒ 4 x 2 − 4 x + 4 = 49 x .............. 1

Solving the equation (1) by factorization method.

4 x 2 − 64 x − x + 16 = 0 ⇒ 4 x x − 16 − 1 x − 16 = 0 ⇒ x − 16 4 x − 1 = 0 ⇒ x = 16, 14

The fraction value can be neglected as count cannot be a fraction.
Thus, the total number of swans is 16.
Hence the correct option is 1.

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Out of a group of swans 72 times the square root of the total number are playing on the shore of a pond. The two remaining ones are swimming in water. Find the total number of swans.