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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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