Question

4. The sum of the digits of a two-digit number is 15: The number obtained by interchanging its
digits exceeds the given number by 9. Find the original number.
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Answer 1

Let the number be xy.

Given,the sum of the digits of a two digit number is 15.

x+y = 15 ...(1)

Also, if the digits are interchanged the result exceeds the original number by 9.

10y+x=10x+y+9

10y+x-10x-y=9

9y-9x=9

y-x=1 ...(2)

(1)+(2) => 2y = 16

y = 16/2 = 8

(1) => x+8=15

x=15-8=7

Therefore the given number is 78