Question

the sum of the digits of a two digits number is 13 and the difference between the number and that formed by reversing the digits is 27 . find the number .

Answer 1

Solution -

Let the digit in ones place be x

So, the digit in tens place be 13 - x

Original no. = 10(13 - x) + 1(x)

= 130 - 10x + x

= 130 - 9x

New no. = 10(x) + 1(13 - x)

= 10x + 13 - x

= 9x + 13  [∵By reversing the digits]

According to Question,

New no. - Original no. = 27

(9x + 13) - (130 - 9x) = 27

⇒ 9x + 13 - 130 + 9x = 27

⇒ 18x - 117 = 27

⇒ 18x = 27 + 117

⇒ 18x = 144

⇒ x = 144 / 18

⇒ x = 8

Required Numbers -

Original no. = 130 - 9x = 130 - 9(8)

= 130 - 72 = 58

New no. = 85 [∵By reversing the digits]

Hence, the required number is either 58 or 85

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