Question

The sum of the digits of a two digit no. is 15 . The no. obtained by interchanging its digits exceeds the given no. by 9. Find the no.??

Answer 1

One digit=x,
another digit=15-x
Let x be the tens digit and 15-x is in ones digit.
actual no=10x+15-x=9x+15
When interchanged,=10(15-x)+x=150-10x+x=150-9x
A/q,
9x+15+9=150-9x
9x+9x=150-24
18x=126
x=126/18
x=7
The no.=9*7+15=63+15=78

Answer 2

Let the digit in tens place be x and the digit in one's place be y.

Then the original fraction = 10x + y.

Given that sum of digits of a two digit number = 15.

= > x + y = 15.  ----- (1)

Given that the number obtained by interchanging its digits exceeds by 9.

= > 10y + x = 10x + y + 9

= > 10y + x - 10x - y = 9

= > -9x + 9y = 9

= > 9y - 9x = 9

= > y - x = 1   ------- (2)

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On solving (1) & (2), we get

= > x + y = 15

= > y - x = 1

    ------------

     2y = 16

         y = 8.

Substitute y = 8 in (1), we get

= > x + y = 15

= > x + 8 = 15

= > x = 7.

Therefore, the required 2-digit number = 78.

hope it helps!