Question

The sum of the digits of a two-digit
number is 4. The sumber got by
changing the digits is 18 less than the
Original number. What is the number ​

Answer 1

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

• Sum of digits of 2 digit no. = 4
• The number got by interchanging the digits is 18 less then the original one .

⠀⠀⠀⠀

______________________

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

• Original number = ??

______________________

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

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

Acc to 1st statement :-

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x + y = 4 ----- ( i )

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Acc. to 2nd statement :-

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10y + x + 18 = 10x + y

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10x - x - 10y + y = 18

⠀⠀⠀⠀

9x - 9y = 18

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9 ( x - y ) = 18

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x - y = 18 / 9

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

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• Adding eq ( i ) and ( ii )

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x + y + x - y = 2 + 4

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2x = 6

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x = 6 / 2

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x = 3

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• putting value of x in eq ( i )

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x + y = 4

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3 + y = 4

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y = 4 - 3

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y = 1

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• finding the no.

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10x + y

⠀⠀⠀⠀

10× 3 + 1

⠀⠀

30 + 1

⠀⠀

31

______________________

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

• Therefore required number is 31

Answer 2

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

Sum of digits of 2 digit no. = 4

The number got by interchanging the digits is 18 less then the original one .

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

Original number = ??

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

let the original number be 10x + y

no. got by reversing the digits = 10y + x

Acc to 1st statement :-

x + y = 4 ----- ( i )

Acc. to 2nd statement :-

⟹ 10y + x + 18 = 10x + y

⟹ 10x - x - 10y + y = 18

⟹ 9x - 9y = 18

⟹ 9 ( x - y ) = 18

⟹ x - y = 18 / 9

⟹ x - y = 2 ------ ( ii )

Adding eq ( i ) and ( ii )

⟹ x + y + x - y = 2 + 4

⟹ 2x = 6

⟹ x = 6 / 2

⟹ x = 3

putting value of x in eq ( i )

⟹ x + y = 4

⟹ 3 + y = 4

⟹ y = 4 - 3

⟹ y = 1

finding the no.

⟹ 10x + y

⟹ 10× 3 + 1

⟹ 30 + 1

⟹ 31

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

Therefore required number is 31.