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, total number of camels = 36.