Question

The sum of the digits of a two digit number is 7.The number obtained by interchanging the digits exceeds the original number by 27.Find the number.

Answer 1

Let the digit in ones place be x

So, the digit in tens place be (7 - x)

Original No. = 10(7 - x) + 1(x)

= 70 - 10x + x

= 70 - 9x

New No. = 10(x) + 1(7 - x)

= 10x + 7 - x

= 9x + 7 【By Interchanging the digits】

According to Question,

New No. - Original No. = 27

(9x + 7) - (70 - 9x) = 27

⇒ 9x + 7 - 70 + 9x = 27

⇒ 18x - 63 = 27

⇒ 18x = 27 + 63

⇒ 18x = 90

⇒ x = 90 / 18

⇒ x = 5

Required Numbers -

Original No. = 70 - 9x = 70 - 9(5)

= 70 - 45 = 25

New No. = 52

【By Interchanging Digits】

Hence, the required number is either 25 or 52

✪ Be Brainly ✪

Answer 2

The number required is 25 or 52.