Question

Sum of the digits of a two-digit number is 8.
When we interchange the digits, it is found that the resulting new number is greater than the original number by 36.
What is the two-digit number?

Answer 1

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Sum of digits of 2 digit no = 8
• number formed by interchanging the digits is 36 greater than the original

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• original no. = ???

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

• let the original no. be 10x + y
• no. formed by reversing the digits = 10y + x

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Acc. to the 1st condition :-

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x + y = 8 ------ ( i )

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Acc. to the 2nd condition :-

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10x + y + 36 = 10y + x

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10y - y - 10x + x = 36

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9y - 9x = 36

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9 ( y - x ) = 36

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y - x = 36 / 9

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y - x = 4 ------ ( ii )

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• Adding eq ( i ) and ( ii )

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x + y + y - x = 8 + 4

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2y = 12

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y = 12 / 2

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y = 6

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• putting the value of y in eq ( i )

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x + y = 8

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x + 6 = 8

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x = 8 - 6

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x = 2

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• finding the digit

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10x + y

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10 × 2 + 6

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20 + 6

⠀⠀⠀⠀

26

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Original number = 26