Question

The sum of the digits of a 2 digit number is 15. The number obtained by interchanging the digits exceeds the given no. By 9. Find the number graphically

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 .

Answer 2

Answer:

First digit = x

Second digit = 15 - x

Original number = 10 × x + 15 - x

= 10x + 15 - x

= 9x + 15

Interchanging = 10(15 - x) + x

= 150 - 10x + x

= 150 - 9x

9x + 15 + 9 = 150 - 9x

9x + 9x = 150 - 15 - 9

18x = 126

x = 126

18

x = 7

so, original number is, 9 × 7 + 15

63 + 15

78

78 IS YOUR ANSWER.

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