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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
`\implies` 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 + x2 = 60x + 180
x2 + 3x – 180 = 0
(x + 15)(x – 12) = 0
x = –15, 12
But, the number of oranges cannot be negative.
So, x = 12.
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