In a 2-digit number, the unit's digit is 5 more than the ten's digit. If 5 times the given number is 24 more than two times the number obtained by interchanging the digits of the given number, then the given number is:

Question

Accepted Answer

Let the ten's digit of the number be $$ x $$. Then, the unit's digit will be $$ x + 5 $$.  
The two-digit number can be expressed as:  
$$
10x + (x + 5) = 11x + 5
$$

The number obtained by interchanging the digits is:  
$$
10(x + 5) + x = 10x + 50 + x = 11x + 50
$$

According to the problem:  
$$
5 	imes (11x + 5) = 24 + 2 	imes (11x + 50)
$$

Simplify:  
$$
55x + 25 = 24 + 22x + 100
$$  
$$
55x - 22x = 100 + 24 - 25
$$  
$$
33x = 99 \implies x = 3
$$

The given number is:  
$$
11x + 5 = 11(3) + 5 = 33 + 5 = 38
$$

Thus, the correct answer is **(c) 38**.

Answer

Answer

Answer