Question

The sum of the digits of two digit number is 12.If the new number formed by reversing the digits is greater than the original by 18, find the original number.plz do not cheat answer from topper because i know that you all are genius

Answer 1

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

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• Sum of the digits of 2 digit no. = 12
• The new number formed by reversing the digits is greater than the original by 18

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

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• The original number = ??

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

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Let the original number be 10x + y

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Acc. to the first condition :-

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X + Y = 12 --- ( i )

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Acc. to the second condition :-

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Reversed number = 10y + x

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10x + y + 18 = 10y + x

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10y - y - 10x + x = 18

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9y - 9x = 18

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9 ( y - x ) = 18

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y - x = 18 / 9

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y - x = 2 ---- ( ii )

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• Adding eq ( i ) and ( ii )

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x + y + y - x = 2 + 12

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y + y = 2 + 12

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2y = 2 + 12

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2y = 14

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y = 14 / 2

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y = 7

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• putting value of y in eq ( i )

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x + y = 12

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x + 7 = 12

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x = 12 - 7

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x = 5

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• Putting values in the original no.

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Original no. = 10x + y

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Original no. = 10 × 5 + 7

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Original no. = 50 + 7

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Original no. = 57

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

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• Original number is 57