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# A Two Digit Number is Such that the Product of the Digits is 16. When 54 is Subtracted from the Number the Digits Are Interchanged. Find the Number - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

#### Question

A two digit number is such that the product of the digits is 16. When 54 is subtracted from the number the digits are interchanged. Find the number

#### Solution

Let the two digits be:

Tens digits be x and units = 16/x

Number =10x+16/x

Number obtained by interchanging =10xx16/x+x

rArr(10x+16/x)-(10xx16/x+x)=54

rArr10x+16/7-160/x+x=54

⇒ 10x2 + 16 - 160 - x2 = 54x

⇒ 9x2 - 54x - 144 = 0

⇒ x2 - 6x - 16 = 0

⇒ x2 - 8x + 2x - 16 = 0

⇒ x(x - 8) + 2(x - 8) = 0

⇒ (x - 8)(x + 2) = 0

⇒ x - 8 = 0

⇒ x = 8

Or

⇒ x + 2 = 0

⇒ x = -2

But, a digit can never be negative, hence x = 8

Hence the required number =10x+16/x=10(8)+16/8=80+2=82

Is there an error in this question or solution?

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Solution A Two Digit Number is Such that the Product of the Digits is 16. When 54 is Subtracted from the Number the Digits Are Interchanged. Find the Number Concept: Solutions of Quadratic Equations by Factorization.
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