Quadratic Equations

Question

A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more books for the same amount, each book would have cost Rs. 1 less. How many books did he buy?

Solution

Let the number of books bought be x. Then,
Cost of x books = Rs. 80
$rightwards double arrow$ Cost of one book = Rs. $open parentheses 80 over straight x close parentheses$
If the number of books bought is x + 4, then
Cost of one book = Rs. $space open parentheses fraction numerator 80 over denominator straight x plus 4 end fraction close parentheses$
According to given condition,
∴ $80 over straight x minus fraction numerator 80 over denominator straight x plus 4 end fraction equals 1$
$rightwards double arrow$    $space space 80 open parentheses 1 over straight x minus fraction numerator 1 over denominator straight x plus 4 end fraction close parentheses space equals space 1$
$rightwards double arrow space space space space space space space space space space 80 open curly brackets fraction numerator straight x plus 4 minus straight x over denominator straight x left parenthesis straight x plus 4 right parenthesis end fraction close curly brackets equals 1$
$rightwards double arrow$    $fraction numerator 320 over denominator straight x squared plus 4 straight x end fraction equals 1$
$rightwards double arrow$ $straight x squared plus 4 straight x equals 320$
$rightwards double arrow$ $straight x squared plus 4 straight x minus 320 space equals space 0$
$rightwards double arrow space space space straight x squared plus 20 straight x minus 16 straight x minus 320 space equals space 0$
$rightwards double arrow$ $straight x left parenthesis straight x plus 20 right parenthesis minus 16 left parenthesis straight x plus 20 right parenthesis space equals 0$
$rightwards double arrow space space space space space space space space space space space space space space space space space space space space left parenthesis straight x plus 20 right parenthesis space left parenthesis straight x minus 16 right parenthesis space equals space 0$
$rightwards double arrow$    $space straight x equals negative 20$
or    $straight x equals 16$
$rightwards double arrow$    $straight x equals 16$
[∵ x cannot be negative]
Hence, the number of books is 16.

Some More Questions From Quadratic Equations Chapter

Check whether the following are quadratic equations:
(x + 2)³ = 2x(x² – 1)

Check whether the following are quadratic equations:
x³ – 4x² – x + 1 = (x – 2)³.

Represent the following problem situations in the form of quadratic equations:
The product of two consecutive positive integers is 306. We need to find the integers.

Represent the following problem situations in the form of quadratic equations:
Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

For Daily Free Study Material Join wiredfaculty

Quadratic Equations

A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more books for the same amount, each book would have cost Rs. 1 less. How many books did he buy?

Some More Questions From Quadratic Equations Chapter

Check whether the following are quadratic equations:
(x + 2)³ = 2x(x² – 1)

Check whether the following are quadratic equations:
x³ – 4x² – x + 1 = (x – 2)³.

Represent the following problem situations in the form of quadratic equations:
The product of two consecutive positive integers is 306. We need to find the integers.

Represent the following problem situations in the form of quadratic equations:
Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

Find the roots of the following quadratic equations by factorisation method:
x² – 3x – 10 = 0

Find the roots of the following quadratic equations by factorisation method:
2x² + x – 6 = 0

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location

For Daily Free Study Material Join wiredfaculty

Quadratic Equations

A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more books for the same amount, each book would have cost Rs. 1 less. How many books did he buy?

Some More Questions From Quadratic Equations Chapter

Check whether the following are quadratic equations:(x + 2)3 = 2x(x2 – 1)

Check whether the following are quadratic equations:x3 – 4x2 – x + 1 = (x – 2)3.

Represent the following problem situations in the form of quadratic equations:The product of two consecutive positive integers is 306. We need to find the integers.

Represent the following problem situations in the form of quadratic equations:Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

Find the roots of the following quadratic equations by factorisation method:x2 – 3x – 10 = 0

Find the roots of the following quadratic equations by factorisation method:2x2 + x – 6 = 0

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Check whether the following are quadratic equations:
(x + 2)³ = 2x(x² – 1)

Check whether the following are quadratic equations:
x³ – 4x² – x + 1 = (x – 2)³.

Represent the following problem situations in the form of quadratic equations:
The product of two consecutive positive integers is 306. We need to find the integers.

Represent the following problem situations in the form of quadratic equations:
Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

Find the roots of the following quadratic equations by factorisation method:
x² – 3x – 10 = 0

Find the roots of the following quadratic equations by factorisation method:
2x² + x – 6 = 0