Question

The sum of digits of a two-digit number is 15. The number obtained by interchanging the digits exceeds the given number by 9. Find the number.

Answer 1

Step-by-step explanation:

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Let the units digit be 'x'

Let the tens digit be 'y'

Then,

Number = 10x + y

Given that sum of the digits is 15

So, x+ y = 15

x = 15 - y --------------------eqn(1)

According to problem, the number formed by interchanging the digits exceeds the original number by 9

So,

10y + x = 10x + y + 9

10y - y - 9 = 10x - x

9y - 9 = 9x

9x - 9y = 9

9(x - y ) = 9

x - y = 9/9

x - y = 1

From equation 1 we found that x = 15 - y

Substitute x = 15- y in above equation

15 - y - y = 1

15 - 2y = 1

- 2y = 1 - 15

-2y = -14

y = -14/-2

y = 7

Now,put y = 7 in equation 1

x = 15 - y

x = 15 - 7

x = 8

Number = 10x + y

= 10(8) + 7

= 80 + 7

= 87