Question

sum of a digit of a two digit number is 5 when we interchange the digit it is found that the resulting new number is less than the original number by 27 what is the two digit number?​

Answer 1

Answer:

41

Step-by-step explanation:

4+1=5

if we interchange the digits, we get:

14(41-27)

Answer 2

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

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• Sum of 2 digits of 2 digit no. = 5
• if we interchange the digits the reulting ni. is 27 less then the original no.

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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 original number be 10x + y

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Acc. to the 1st statement :-

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x + y = 5 ---- ( i )

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Interchange no. = 10y + x

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Acc. to the 2nd statement :-

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10x + y = 10y + x + 27

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10x - x - 10y + y = 27

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9x - 9y = 27

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9 ( x - y ) = 27

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x - y = 27 / 9

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x - y = 3 ---- ( ii )

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• Adding eq ( i ) and ( ii )

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x + y + x - y = 5 + 3

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x + x = 5 + 3

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2x = 8

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x = 8 / 2

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x = 4

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• Putting value of x in eq ( i )

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x + y = 5

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4 + y = 5

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y = 5 - 4

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y = 1

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• Finding the original no.

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10x + y

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10 x 4 + 1

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40 + 1

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41

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

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• Original number = 41