Question

The sum of a two digit number and number obtained on reversing the digits is99. If the number obtained on reversing the digit is 9 more than the original number,find the number.

Answer 1

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

Number = 10y +x

The number obtained by reversing the order of the digits is = 10x +y

ATQ
10y +x + 10x +y= 99
x + 10x +10y +y = 99
11x + 11y= 99
11(x+y) = 99
x +y = 99/11

x +y = 9………………..(1)

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

x - y = 1………………….(2)

On adding eqs 1 and 2
x +y = 9
x - y = 1
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2x = 10
x = 10/2

x = 5

On putting x = 5 in equation 2
x - y = 1
5 -y = 1
-y = 1-5
-y = -4
y = 4

Number= 10y +x = 10(4)+5= 40 +5= 45

Hence , the number is 45.

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