Question

The sum of a number of two digits and of the number formed by reversing the digits is 110 and the difference of the digits is 6 . Find the number.

Answer 1

Here is your solution


Let,
The ten's digit of original number be x

The unit's digit of the original number be y

The original number= 10x + y

The Number obtained on reversing the digits = 10y + x

A/q

Add original numbers and reverse number.

So

=>( 10x + y )+( 10y + x )=110 .

=>11x + 11y = 110

=>11( x + y ) = 110

=>x + y = 110/11

x + y = 10...............(i)


x - y = 6 ..................(ii) (given)

On adding equation (i) and (ii), we get

x + y + x - y= 10 +6

2x = 16
X=8


On putting the value of x in equation (i), we get

x + y = 10

8 + y = 10 .

Y = 10 - 8

y= 2


original number = 10x + y .
=>10 × 8 + 2 .
=>80 + 2 .
=>82

Hence,
The required number is 82 .

Hope it helps you