# The sum of the digits of a two – digit number is 15. The number obtained by interchanging the digits exceeds the given number by 9. The number isA. 96B. 69C. 87D. 78

Let us assume the tens and the unit digits of the required number be x and y respectively

Required number = (10x + y)

According to the given condition in the question, we have

x + y = 15 (i)

By reversing the digits, we obtain the number = (10y + x)

(10y + x) = (10x + y) + 9

10y + x – 10x – y = 9

9y – 9x = 9

y – x = 1 (ii)

Now, on adding (i) and (ii) we get:

2y = 16

Putting the value of y in (i), we get:

x + 8 = 15

x = 15 – 8

x = 7

Required number = (10x + y)

= 10 × 7 + 8

= 70 + 8

= 78

Hence, option D is correct

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