Correct Answer - Option 4 : 7
Given:
2-digit numbers which have difference between the original two-digit number and the one obtained from reversing the digits equal to 27.
Concepts used:
Original 2-digit number = 10x + y
Number obtained after reversing digits = 10y + x
Calculation:
Let the original number be xy.
⇒ Original 2-digit number = 10x + y
When digits x and y are reversed in position,
Resulting number after reversing digits = 10y + x
Difference between the original two-digit number and the one obtained from reversing the digits is 27.
⇒ 10y + x – (10x + y) = 27
⇒ 9y – 9x = 27
⇒ y – x = 3
Possible numbers that satisfy above equation are: 63, 52, 30, 41, 74, 85 and 96.
∴ There are 7 possible 2-digit numbers.
