Question

The sum of the digits of a two digit number is
12. If the new number formed by reversing the
digits is greater than the original number by 54,
find the original number.​

Answer 1

❒ Let the two digits be x and y respectively. The number is (10x + y). After, reversing the digits obtained number is (10y + x).

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$\underline{\boldsymbol{According\: to \:the\: Question :}}$

• The sum of the digits of two digit number is 12.

$:\implies\sf x + y = 12 \qquad\bigg\lgroup\bf Equation (I) \bigg\rgroup$

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Now,

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$:\implies\sf 10y + x - 10x - y = 54 \\\\\\:\implies\sf 9y - 9x = 54 \\\\\\:\implies\sf y - x = \cancel\dfrac{54}{9}\\\\\\:\implies\sf y - x = 6\\\\\\:\implies\sf y = 6 + x$

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$\underline{\bf{\dag} \:\mathfrak{From\: equation (I)\: :}}$⠀

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$:\implies\sf x + y = 12 \\\\\\:\implies\sf x + 6 + x = 12 \qquad\bigg\lgroup\bf y = 6 + x \bigg\rgroup \\\\\\:\implies\sf 2x + 6 = 12\\\\\\:\implies\sf 2x = 12 - 6\\\\\\:\implies\sf 2x = 6\\\\\\:\implies\sf x = \cancel\dfrac{6}{2}\\\\\\:\implies{\underline{\boxed{\sf{\pink{ x = 3}}}}}$

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$\underline{\bf{\dag} \:\mathfrak{Substituting \; value \: of \: x \: :}}$⠀⠀⠀⠀

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Therefore,

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$:\implies\sf y = 6 + x \\\\\\:\implies\sf y = 6 + 3\\\\\\:\implies{\underline{\boxed{\sf{\pink{y = 9}}}}}$

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$\therefore{\underline{\sf{Hence, \; the \: original \; number \; is \; \bf{ 39}.}}}$

Answer 2

hello

quesion ⤵️

The sum of the digits of a two digit number is

12. If the new number formed by reversing the

digits is greater than the original number by 54,

find the original number.

given↙️

two digit number is12

new number formed by reversing the

digits is greater than the original number by 54,

to. find

find the original number.

answer

39.

solusion ⬇️

according to. question

Let the digits be x and y, so the number will be = (10x+y), on reversing the digits, the new number will be = (10y+x)

According to the question we can write as x + y=12 and also we can write as 10y+x-10x-y=54

Which implies 9y-9x=54

y-x=54/9

y-x=6

y=6+x

Now on substituting this in x + y=12 we get

x+6+x=12

2x+6=12

2x=12-6

x=6/2=3

Now y=6+x=6+3=9

So the number is 39

To check: digit sum=3+9=12

Reversing the digit numbers becomes 93 and 93-39=54

Hence verified.

hope. it's. helps. you