# Q. The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54.

1. The sum of the two digits of a number can be determined only if the product of the two digits is known.

2. The difference between the two digits of the number can be determined.

Which of the above statements is/are correct?

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

Correct Answer: (b) 2 only

#### Question from UPSC Prelims 2021 CSAT Paper

**Explanation : **

## Analysis of 2-Digit Number

Let’s say the 2-digit number is 10x + y where x and y are the tens and units digits respectively. When we interchange the positions of the digits, we get a new number: 10y + x. The difference between these two numbers is given as 54.

So we have: (10x + y) – (10y + x) = 54

9x – 9y = 54

x – y = 6

From this equation, we can determine that the difference between the two digits of the number is 6. So statement 2 is correct.

However, knowing only that x – y = 6 does not allow us to determine the sum of the two digits without additional information. So statement 1 is incorrect.