Question

The digits of a 2 digit number differ by 5.if the digits are inter changed and the resulting number is added to the original number we get99. find the original number

Answer 1

Solution -

Let the digit in ones place be x

So, the digit in tens place be x + 5

Original no. = 10(x + 5) + 1(x)

= 10x + 50 + x

= 11x + 50

New no. = 10(x) + 1(x + 5)

= 10x + x + 5

= 11x + 5      [By reversing the digits]

According to Question,

Original no. + New no. = 99

⇒ (11x + 50) + (11x + 5) = 99

⇒ 22x + 55 = 99

⇒ 22x = 99 - 55

⇒ 22x = 44

⇒ x = 44 / 22

⇒ x = 2

Required Numbers -

Orginal no. = 11x + 50 = 11(2) + 50

= 22 + 50 = 72

New no. = 27   [By reversing the digits]

Hence, the required number is either 72 or 27

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