Question

the sum of two digit and the number obtained by interchanging of digit , if 12 is added to the number the new number becomes five times the sum of digit​

Answer 1

$\bold{Correct\: Question\::}$

The sum of two digit and the number obtained by interchanging of digit is 132 . If 12 is added to the number the new number becomes five times the sum of digit. Find the number.

Solution:

• Let ten's digit be M and one's digit be N.

Original number = 10M + N

Interchanged number = 10N + M

» The sum of two digit and the number obtained by interchanging of digit is 132.

=> 10M + N + 10N + M = 132

=> 11M + 11N = 132

=> M + N = 12

=> M = 12 - N ________ (eq 1)

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» if 12 is added to the number the new number becomes five times the sum of digit.

=> 12 + 10M + N = 5 × (sum of numbers i.e. M + N)

=> 12 + 10M + N = 5 × 12

=> 12 + 10M + N = 60

=> 10M + N = 60 - 12

=> 10M + N = 48

=> 10(12 - N) + N = 48

=> 120 - 10N + N = 48

=> - 9N = - 72

=> N = 8

• Put value of N in (eq 1)

=> M = 12 - 8

=> M = 4

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Number = 10M + N

=> 10 × 4 + 8

=> 48

______________ [ANSWER]