Question

the sum of two digit number is 15 the number obtained by reversing the order of the digit of a given number exceeds the number given by 9 find the number

Answer 1

Let the digit at ten's place be x and one's place be y

So , x + y = 15 -------(i), x + y - 15 = 0

Original Number , = 10x + y

Reversing = 10y + x

According to Question,

10x + y + 9 = 10y + x

9 = 9y - 9x

9 = 9(y - x)

y - x = 1------ (ii)

(i)  + (ii) , gives

x + y + y - x = 1 + 15 = 16

2y = 16 , y = 8

Applying value of y in (ii)

y - x = 1 , 8 -x = 1 = x = 7

Number , 10x  + y = 10*7 + 8 = 78

The number is 78

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