Question

35. The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting
number is added to the original number, we get 143. What can be the original number?
OR
Present ages of Anu and Raj are in the ratio 4:5. Eight years from now the ratio of their ages will​

Answer 1

*Second question is incomplete

35) Answer:

Original number is 85.

Step-by-step explanation:

$\bold{\underline{\underline{Assume\::}}}$

Let the -

• Ten's digit be M
• One's digit be N

We have

Original number = 10M + N

Revered number = 10N + M

$\bold{\underline{\underline{Solution\::}}}$

According to question,

The two digits number are differ by 3.

$\implies\:M\:-\:N\:=\:3$

$\implies\:M\:=\:3\:+\:N$  ____ (eq 1)

If the digit are interchanged and the resulting number is added to the original number, we get 143.

$\implies\:10N\:+\:M\:+\:10M\:+\:N\:=\:143$

$\implies\:11N\:+\:11M\:=\:143$

$\implies\:N\:+\:M\:=\:13$

$\implies\:N\:+\:3\:+\:N\:=\:13$

[From (eq 1)]

$\implies\:2N\:=\:10$

$\implies\:N\:=\:5$

Substitute value of N in (eq 1)

$\implies\:M\:=\:3\:+\:5$

$\implies\:M\:=\:8$

Original number = 10M + N

⇒ 10(8) + 5

⇒80 + 5

⇒85

∴ Original number is 85.

Answer 2

Answer:

Suppose one digit = N

and the ten's digit = M.

the ten's digit = M.Revered number = 10N + M.

Original number = 10M + N .

Original number = 10M + N .The digits of a two number differ by 3 .

Original number = 10M + N .The digits of a two number differ by 3 .= M - N = 3.

Original number = 10M + N .The digits of a two number differ by 3 .= M - N = 3.M = 3 + N ........(eq1).

If the digits are interchanged and the resulting number is added to the original number , we get 143 .

= 10N + M + 10M + N = 143 .

= 11N + 11M = 143 .

= N + M = 13 .

= N + 3 + N = 13 .

Solving (eq1) .

2N = 10

N = 5 . N = 10 = 5 .

2

Substitute value of N in (eq1):

M = 3 + 5

M = 8 .

Original number = 10M + N

= 10(8)+ 5 .

= 80 + 5 .

= 85 .

Thus Original number = 85 .