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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

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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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