Question

The sum of the digits of a 2 no is 8 .The number obtained by interchanging the digits exceeds the given no. by 18.Find the given no. ​

Answer 1

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Given:

The sum of the digits of a two number is 8. The number obtained by interchanging the digits exceeds the given number by 18.

To find:

The given number.

Explanation:

Let the digit at unit's place be R &

Let the digit at ten's place be M

∴The original number= 10M +R

According to the question:

→ R + M= 8..................(1)

Number obtained by interchanging the digits= 10R+ M

→ 10R+ M = 10M+ R+18

→ 10R -R +M -10M =18

→ 9R -9M =18

→ R - M= 2..............................(2)

• Using Substitution Method:

From equation (1),we get;

⇒ R + M= 8

⇒ R = 8 - M..........................(3)

Therefore,

Putting the value of R in equation (2),we get;

⇒ 8 - M -M =2

⇒ 8 -2M =2

⇒ -2M = 2- 8

⇒ -2M = -6

⇒ M = $\cancel{\frac{-6}{-2} }$

⇒ M = 3

Now,

Putting the value of M in equation (3), we get;

⇒ R = 8 - 3

⇒ R =5

Thus,

The original number is 10(3) + 5

∴The original number is 30+5= 35.

Answer 2

$\bold{\large{\underline{\underline{\sf{AnsWer :}}}}}$

The original number is 35

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Let the digit at unit's place be = R

Let the digit at ten's place be = M

∴The original number = 10M +R

According to the question:

→ R + M= 8________________(1)

Number obtained by interchanging the digits= 10R+ M

→ 10R+ M = 10M+ R+18

→ 10R -R +M -10M =18

→ 9R -9M =18

→ R - M= 2______________(2)

Using Substitution Method:

From equation (1),we get;

⇒ R + M= 8

⇒ R = 8 - M_______________(3)

Therefore,

Putting the value of R in equation (2),we get;

⇒ 8 - M -M =2

⇒ 8 -2M =2

⇒ -2M = 2- 8

⇒ -2M = -6

⇒ $M = \cancel{\frac{-6}{-2} }$

⇒ M = 3

Now,

Putting the value of M in equation (3), we get;

⇒ R = 8 - 3

⇒ R =5

Thus,

The original number is 10(3) + 5

∴The original number is 30+5= 35.