Correct Answer - Option 3 : 42
Let the number be (10x + y), where 'x' is the digit at tens place and 'y' is the digit at ones place.
The total sum of the digits of any two-digit number is 6.
According to the question:
x + y = 6 __________ (1)
After interchanging the digits, the new number we get is 10y+x.
If the place of digits in this number is mutually changed, then there is a difference of 18 between the new number and the first number thus obtained.
According to question:
10x + y - (10y + x) = 18
⇒ 10x + y - 10y - x = 18
⇒ 9x - 9y = 18
⇒ 9 (x - y) = 18
⇒ x - y = 18 ÷ 9
⇒ x - y = 2
⇒ x = 2 + y
Putting the value of x in equation (1), we get:
2 + y + y = 6
⇒ 2y = 6 - 2
⇒ 2y = 4
⇒ y = 4 ÷ 2
⇒ y = 2
So, x = 2 + 2 (As, x = 2 + y and y = 2)
⇒ x = 4
Therefore, the number is: 10 × 4 + 2
= 40 + 2
= 42
Hence, ‘42’ is the correct answer.