To find the remainder when a number is divided by 24, we need to understand the concept of divisibility rules and apply them to the given situation.

Divisibility Rule for 24:
To determine if a number is divisible by 24, we need to check if it is divisible by both 8 and 3.

1. Divisibility by 8:
A number is divisible by 8 if the last three digits of the number form a multiple of 8.

2. Divisibility by 3:
A number is divisible by 3 if the sum of its digits is divisible by 3.

In this case, the number leaves a remainder of 31 when divided by 48. Let's assume the number is N.

Finding the Divisibility by 8:
Since 48 is divisible by 8, we need to check if the remainder 31 is also divisible by 8. If it is, then the number N is also divisible by 8.

The remainder 31 is not divisible by 8, so we can conclude that N is not divisible by 8.

Finding the Divisibility by 3:
To find the remainder when N is divided by 24, we need to check if the sum of its digits is divisible by 3.

Since the remainder when N is divided by 48 is 31, we can write N as 48x + 31, where x is an integer.

The sum of the digits of N is equal to the sum of the digits of 48x + 31. Let's assume the sum of the digits is S.

We know that 48x is divisible by 3 since 48 is divisible by 3. Therefore, the divisibility of N by 3 depends on the divisibility of 31 by 3.

The sum of the digits of 31 is 3 + 1 = 4, which is not divisible by 3.

Therefore, we can conclude that the remainder when N is divided by 24 is the same as the remainder when N is divided by 48, which is 31.

Hence, the correct answer is option B) 7.