Advertisements
Advertisements
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.
Advertisements
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.
RELATED QUESTIONS
The sum of the ages of Vivek and his younger brother Amit is 47 years. The product of their ages in years is 550. Find their ages.
A stone is thrown vertically downwards and the formula d = 16t2 + 4t gives the distance, d metres, that it falls in t seconds. How long does it take to fall 420 metres?
A hotel bill for a number of people for overnight stay is Rs. 4800. If there were 4 people more, the bill each person had to pay, would have reduced by Rs. 200. Find the number of people staying overnight.
Rs. 6500 was divided equally among a certain number of persons. Had there been 15 persons more, each would have got Rs. 30 less. Find the original number of persons.
Mohan takes 16 days less than Manoj to do a piece of work. If both working together can do it in 15 days, in how many days will Mohan alone complete the work?
The ages of two sisters are 11 years and 14 years. In how many years’ time will the product of their ages be 304?
The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present ages.
Rs. 480 is divided equally among ‘x’ children. If the number of children were 20 more, then each would have got Rs. 12 less. Find ‘x’.
Two years ago the ages of Radha and Meena were in the ratio 5 : 2. If the sum of their present ages is 39 years, their ages, 2 years ago, were ______.
₹ 320 were divided equally among 8 children. If 2 more children join them, each will get, how many rupees more or less?
