Question

6. The sum of digits of a 2-digit number is 11. If the number obtained by reversa,
digits is 9 less than the original number, find the number.
che digit number and the number obtained he
S.​

Answer 1

$\bf{\dag}\:\underline{\frak{Corrected\; Question :}}$

• The sum of digits of a 2-digit number is 11. If the number obtained by reversing the digits is 9 less than the original number, find the number.

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$\bf{\dag}\:\underline{\frak{AnswEr :}}$

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❍ Let the unit digit be x and ten's digit be y respectively. $\therefore$ The number is (x + 10y).

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$\underline{\bigstar\:\boldsymbol{According\;to\;the\; Question\; :}}$⠀⠀

Case I)

• The sum of digits of a two digits number is 11. Therefore,

$:\implies\sf x + y = 11 \qquad\quad\bigg\lgroup\bf Equation\;(i)\bigg\rgroup$

⠀

Case II)

• If the number obtained by reversing the digits is 9 less than the original number. And, the number reversing the digits is (y + 10x + 9).

$:\implies\sf y + 10x + 9 = x + 10y \\\\:\implies\sf 10x + y - 10y - x = -9\\\\:\implies\sf 9x - 9y = -9\\\\:\implies\sf x - y = -1\qquad\quad\bigg\lgroup\bf Equation\;(ii)\bigg\rgroup$

• By using Both Equations (I) & (II).

$:\implies\sf x + y = 11\\\\:\implies\sf x - y = -1\\\\:\implies\sf 2x = 10\\\\:\implies\sf x = \cancel\dfrac{10}{2}\\\\:\implies{\underline{\boxed{\frak{\pink{x = 5}}}}}\;\bigstar$

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• By using Equation (I). Therefore,

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$:\implies\sf x + y = 11\\\\:\implies\sf 5 + y = 11\\\\:\implies\sf y = 11 - 5\\\\:\implies{\underline{\boxed{\frak{\pink{y = 6}}}}}\;\bigstar$

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ORIGINAL NUMBER :

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$:\implies\sf Original\; Number = x + 10y\\\\:\implies\sf Original \; Number = 5 + 10(6)\\\\:\implies\sf Original \; Number = 5 + 60 \\\\:\implies{\underline{\boxed{\frak{\purple{65}}}}}\;\bigstar$

$\therefore{\underline{\textsf{Hence,\;the\; original\; number\;is\; \textbf{65 }.}}}$

$\rule{300}2$

V E R I F I C A T I O N :

• We're given with the sum of digits of a two digit number that is 11. Now, let's verify Both the numbers. Therefore,

$:\implies\sf x + y = 11 \\\\:\implies\sf (5) + (6) = 11 \\\\:\implies{\boxed{\underline{\sf{ 11 = 11 }}}}$

$\qquad\quad\therefore{\underline{\textsf{\textbf{Hence Verified!}}}}$

Answer 2

Answer:

Given :-

• The sum of digits of 2 digits number is 11. If the number obtained by reversing the digits is 9 less than the original number.

To Find :-

• What is the number.

Solution :-

Let, the ten's place digits be x

And, the unit's place digits will be y

Then, the number is 10x + y.

And, its obtained by reversing the digits is 10y + x.

According to the question,

↦ 10x + y - (10y + x) = 9

↦ 10x + y - 10y - x = 9

↦ 10x - x - 10y + y = 9

↦ 9x - 9y = 9

➦ x - y = 1 --------- (Equation no 1)

And,

➦ x + y = 11 ----------- (Equation no 2)

Now, by adding the equation no (1) and (2) we get,

⇒ x - y + x + y = 1 + 11

⇒ x + x - y + y = 12

⇒ 2x = 12

⇒ x = 12/2

➠ x = 6

Again, by putting the value of x = 6 in the equation no (2) we get,

⇒ x + y = 11

⇒ 6 + y = 11

⇒ y = 11 - 6

➠ y = 5

Hence, the required number is :

↛ 10x + y

↛ 10(6) + 5

↛ 60 + 5

➤ 65

∴ The number is 65 .