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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