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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. - Algebra

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. 

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Solution

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. 

Concept: Simple Situational Problems
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