Correct Answer - Option 4 : 45
Given :
A two-digit number is reversed and the larger number is divided by the smaller number.
Calculation:
Let the two-digit number by 10x + y
where x denotes tens place and y denotes one's place.
If the number is reversed, we get 10y + x.
Let us say that the tens place is greater than the one's place, which means:
(10x + y) > (10y + x)
For the number to be the highest number, one of the digits must be 9.
This means the tens place digit will be 9.
(10x + y ) = 90 + y ----- original number
( 10y + x ) = 10y + 9 ------ reversed number
If the one's place digit is very small, the remainder will be very small or very large which will lead to a small remainder.
So, we can assume the number to be 4 or 5.
With 4,
Original number = 94
Reversed number = 49
Remainder = 94 / 49 = 45
With 5,
Original number = 95
Reversed number = 59
Remainder = 95 / 59 = 36
∴ The largest possible remainder is 45
