#### Question

Mr. Mehra sends his servant to the market to buy oranges worth Rs 15. The servant having eaten three oranges on the way. Mr. Mehra pays Rs 25 paise per orange more than the market price.

Taking x to be the number of oranges which Mr. Mehra receives, form a quadratic equation in x. Hence, find the value of x.

#### Solution

Number of oranges = y

Cost of one orange = Rs 15/y

The servant ate 3 oranges so Mr. Mehra received (y - 3) oranges.

So x = y - 3 => y = x + 3 ....(1)

The servant ate 3 oranges, so Mr. Mehra received (y - 3) oranges.

So x = y - 3 => y = x + 3 ....(1)

Cost of one orange paid by Mr. Mehra = Rs `15/y + 0.25`

`= Rs 15/(x + 3) + 1/4` [Using (1)]

Now Mr. Mehra pays a total of Rs 15

`(15/(x + 3) + 1/4) xx x = 15`

`(60 + x + 3)/(4(x + 3)) xx x = 15`

`63x + x^2 = 60x + 180`

`x^2 = 3x - 180 = 0`

(x + 15)(x - 12) = 0

x = -15,12

But the number of oranges cannot be negative So x = 12