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.

Answer 1

Let x be the total number of camels.

Number of camels seen in the forest = `x/(4)`

Number of camels gone to mountain = 2`sqrt(x)`

Number of camels on the bank of  river = 15

Total number of camels = `x/(4) + 2sqrt(x) + 15 = x`

⇒ x + 8`sqrt(x)` + 60 = 4x

⇒ 3x − 8`sqrt(x)` − 60 = 0

Put `sqrt(x) = y`

⇒ 3y² − 8y − 60 = 0

⇒ 3y² − 18y + 10y − 60 = 0

⇒ 3y(y = 6) + 10(y − 6) = 0

⇒ (y − 6)(3y + 10) = 0

⇒ y = 6 or 3y + 10 = 0

⇒ y = 6 or y = `-(10)/(3)`

Now y = 6

⇒ `sqrt(x)` = 6

On squaring x = 36.

Hence, the total number of camels = 36.