Question

the digits of a 2 digit number differ by 5.if the digit are interchanged and the resulting number is added to the original number we get 99 find the original number ​

Answer 1

Let the digit at tenth place be x and ones place be y.

A.T.Q,

x - y = 5 ------(i)

10y + x + 10x + y = 99

11y + 11x = 99

x + y = 9

x - y = 5
x + y = 9
--------------
2x = 14
--------------

x = 7

x - y = 5

7 - y = 5

-y = -2

y = 2

Original Number = 72

Answer 2

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Given:

The digits of a two digit number differ by 5.If the digit are interchange and the resulting number is added to the original number we get 99.

To find:

The original number.

Explanation:

Let the unit's digit be M &

Let the ten's digit be R

∴ The original number= 10R+M.

If the digits are interchanged then resulting number=10R+M.

According to the question:

R - M= 5.................(1)

&

→ (10M+R)+ (10R+M)= 99

→ 10R +M +10M+R= 99

→ 10R +R+ M+10M= 99

→ 11R +11M= 99

→ R + M= 9....................(2)

• Using Substitution Method:

From equation (1),we get;

⇒ R - M= 5

⇒ R= 5 +M................(3)

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

⇒ 5+M +M= 9

⇒ 5+ 2M= 9

⇒ 2M = 9 -5

⇒ 2M = 4

⇒ M= $\cancel{\frac{4}{2} }$

∴M= 2

Now,

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

⇒ R= 5+ 2

⇒ R= 7

Thus,

The original number is 10(7)+ 2

The original number is 70+2 = 72.