Question

the sum of the digits of two digit numberis 15 .The number obtained by interchanging the digits exceeds the given number by 9.Find the originsl number​

Answer 1

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

Original number = 10M + N

» The sum of the digits of two digit numberis 15.

=> M + N = 15

=> M = 15 - N _______ (eq 1)

» The number obtained by interchanging the digits exceeds the given number by 9.

Interchanged number = 10N + M

• A.T.Q.

=> 10M + N = 10N + M + 9

=> 10M - M + N - 10N = 9

=> 9M - 9N = 9

=> M - N = 1

=> (15 - N) - N = 1

=> 15 - 2N = 1

=> - 2N = - 16

=> 2N = 16

=> N = 8

Put value of N in (eq 1)

=> M = 15 - 8

=> M = 7

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Number = 10M + N

=> 78

__________ [ANSWER]

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