Question

27A two digit number is such that the product of its digits is 35. If 18 is added to the
number, the digit interchange their places. Find the number.​

Answer 1

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

• Product of the no's = 35
• If 18 is added no. Will interchange its digits

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

• The original no. = ?

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

• let the no. be 10x + y

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Acc. to 1st statement :-

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xy = 35

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Acc. to 2nd statement :-

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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 ------ ( i )

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$\sf{\red{\boxed{\bold{( y + x)^2 - ( y - x)^2 = 4xy }}}}$

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$\sf: \implies\: {\bold{ ( y + x )^2 -( 2 )^2 = 4\times35}}$

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$\sf: \implies\: {\bold{ ( y + x)^2 - 4 = 140}}$

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$\sf: \implies\: {\bold{ ( y + x )^2 = 140 + 4}}$

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$\sf: \implies\: {\bold{ ( y + x )^2 = 144 }}$

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$\sf: \implies\: {\bold{ y + x = \sqrt{144}}}$

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$\sf: \implies\: {\bold{ y + x = 12}}$ ----- ( ii )

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• Adding eq ( i ) and ( ii )

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y - x + y + x = 12 + 2

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2y = 14

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y = 7

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• Putting value of y in eq ( i )

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y - x = 2

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7 - x = 2

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x = 7 - 2

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x = 5

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• finding the original no.

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10x + y

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10 × 5 + 7

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50 + 7

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57

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

• Required number is 57

Answer 2

Answer:

required number is 57......