Question

the sum of a two digit no formed by interchanging the digit132. if 12 is added to the number becomes 5 times .the sum of the digits.find the numbers​

Answer 1

$\sf{\bold{\green{\underline{\underline{Correct\: question}}}}}$

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• The sum of a two-digit number and the number formed by interchanging the digits is 132. If 12 is added to the number, the new number becomes 5 times the sum of the digits. Find the number.

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

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• The sum of 2 digit no. and the no. formed by interchanging its digit is 132
• If 12 is added to the no. the no. becomes 5 times .

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

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• Original no = ?

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

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Let the no. be 10x + y

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No. formed by interchanging its digit is 10y + x

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Acc. to the 1st statement :-

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10x + y + 10y + x = 132

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11x + 11y = 132

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11( x + y ) = 132

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x + y = 132 / 11

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x + y = 12 --- ( i )

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Acc. to the 2nd statement :-

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5 ( x + y ) = 12 + 10x + y

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5x + 5y = 12 + 10x + y

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5y - y - 10x + 5x = 12

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4y - 5x = 12 --- ( ii )

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• Multiplying eq ( i ) by 5

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( x + y = 12 ) × 5

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5x + 5y = 60

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• Adding eq ( ii ) and ( iii )

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4y - 5x + 5x + 5y = 60 + 12

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4y + 5y = 60 + 12

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9y = 72

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y = 72 / 9

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y = 8

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• Putting value of y in eq ( i )

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x + y = 12

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x + 8 = 12

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x = 12 - 8

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x = 4

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• Finding the original no.

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Original no. = 10x + y

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Original no. = 10 × 4 + 8

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Original no. = 40 + 8

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Original no. = 48

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

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• Required number = 48