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
Find the roots of the following quadratic equation by factorisation:
`2x^2 – x + 1/8 = 0`
Solve the following quadratic equations by factorization:
3x2 = -11x - 10
The hypotenuse of a right triangle is `3sqrt10`. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be `9sqrt5`. How long are the legs of the triangle?
Solve the following quadratic equations by factorization:
`(1 + 1/(x + 1))(1 - 1/(x - 1)) = 7/8`
Three consecutive natural numbers are such that the square of the first increased by the product of other two gives 154. Find the numbers.
Solve: x(x + 1) (x + 3) (x + 4) = 180.
Solve the following equation by factorization
x(6x – 1) = 35
The lengths of the parallel sides of a trapezium are (x + 9) cm and (2x – 3) cm and the distance between them is (x + 4) cm. If its area is 540 cm2, find x.
Two pipes running together can fill a tank in `11(1)/(9)` minutes. If one pipe takes 5 minutes more than the other to fill the tank, find the time in which each pipe would/fill the tank.
At t minutes past 2 pm, the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than `t^2/4` minutes. Find t.
