Question

A two digit number is such that the product of its digits is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.

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Solution

Let the tens digit be x. Then, the units digits

equals space 18 over straight x

∴ Number

equals space 10 straight x plus 18 over straight x

and Number obtained by interchanging the digits

space space equals 10 cross times 18 over straight x plus straight x

∴

open parentheses 10 straight x plus 18 over straight x close parentheses minus open parentheses 10 cross times 18 over straight x plus straight x close parentheses space equals space 63

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space space space 10 straight x plus 18 over straight x minus 180 over straight x minus straight x equals 63

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left parenthesis straight x minus 9 right parenthesis space left parenthesis straight x plus 2 right parenthesis space equals space 0

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straight x equals 9 space space or space space straight x space equals space minus 2

So,

straight x equals 9.

Hence, the required number

equals 10 cross times 9 plus 18 over 9 equals 92.

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Quadratic Equations

A two digit number is such that the product of its digits is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.

Some More Questions From Quadratic Equations Chapter

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.

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x² – 3x – 10 = 0

Find the roots of the following quadratic equations by factorisation method:
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John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.

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For Daily Free Study Material Join wiredfaculty

Quadratic Equations

A two digit number is such that the product of its digits is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.

Some More Questions From Quadratic Equations Chapter

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

John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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