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The sum of a two digit number and a number obtained by interchanging the digits is 132. What is the product between the sum and difference of the digits of the number, if the ratio between the digits of the number is 1 : 2?

The sum of a two digit number and a number obtained by interchanging the digits is 132. What is the product between the sum and difference of the digits of the number, if the ratio between the digits of the number is 1 : 2? Correct Answer 48

The number obtained is greater than the number obtained on reversing the digits, thus the ten’s digit is greater than the unit’s digit

Let ten’s digit and unit’s digit be 2x and x respectively

Then, + (10x + 2x) = 132

⇒ 21x + 12x = 132

⇒ 33x = 132

⇒ x = 4

The product between the sum and difference of the digits of the number = (2x + x)(2x – x)

⇒

⇒ 12 × 4 = 48

∴ The product is 48

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