Advertisements
Advertisements
Question
A shopkeeper purchases a certain number of books for Rs. 960. If the cost per book was Rs. 8 less, the number of books that could be purchased for Rs. 960 would be 4 more. Write an equation, taking the original cost of each book to be Rs. x, and Solve it to find the original cost of the books.
Advertisements
Solution
Original cost of each book
= ₹ x
∴ Number of books for ₹960 = `(960)/x`
Now, if cost of each book = ₹(x - 8)
Number of books for ₹960 = `(960)/(x - 8)`
According to the question
`(960)/x + 4 = (960)/(x - 8)`
or
`(960)/((x - 8)) - (960)/x = 4`
`(960x - 960x + 7,680)/(x (x - 8)) = 4`
or
7,680 = 4x2 - 32x
or
x2 - 8x - 1,920 = 0
x2 + 40x - 48x - 1,920 = 0
x (x + 40) - 48 (x + 40) = 0
(x + 40) (x - 48) = 0
⇒ x = -40, 48
as cost can't be - ve x = 48.
RELATED QUESTIONS
Solve the following quadratic equations by factorization:
`7x + 3/x=35 3/5`
Solve each of the following equations by factorization:
`x+1/x=2.5`
The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.
If ax2 + bx + c = 0 has equal roots, then c =
Solve the equation using the factorisation method:
`(3x -2)/(2x -3) = (3x - 8)/(x + 4)`
Solve the following equation by factorization
2x2 – 9x + 10 = 0,when x∈N
Find two consecutive natural numbers such that the sum of their squares is 61.
The length of a rectangle exceeds its breadth by 5 m. If the breadth were doubled and the length reduced by 9 m, the area of the rectangle would have increased by 140 m². Find its dimensions.
A piece of cloth costs Rs. 300. If the piece was 5 metres longer and each metre of cloth costs Rs. 2 less, the cost of the piece would have remained unchanged. How long is the original piece of cloth and what is the rate per metre?
Car A travels ‘x’ km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
- Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.
- If car A uses 4 litres of petrol more than car B in covering 400 km. write down an equation, in A and solve it to determine the number of litres of petrol used by car B for the journey.
