Question

The sum of a two digit number and the number obtained by reversing its digits is 121. Find the number if its units place digit is greater than the tens place digit by 7. 

Answer 1

Suppose, the units place digit of the two digit number is y and the tens place digit is x.
∴ the number is 10x + y
∴ the number obtained by reversing the digits is 10y + x
∴ from the given conditions, 

`(10x+y)+(10y+x)=121` 

∴ 11x+11y=121                                ∴ x+y=11 .............(I)

Also, x=y+7                                      ∴ x-y=7 ................(II) 

∴ Adding (I) and (II), `2x=18       x=9`

∴ from (I) `a+y=11`     `    y=2` 

∴ the two digit number is 29.