A certain number when divided by 45 leaves a remainder 31. What is the remainder if the same number be divided by 15?

Sure, here is the step by step solution:

Step 1: Understand the problem The problem states that there is a number which, when divided by 45, leaves a remainder of 31. We need to find the remainder when the same number is divided by 15.

Step 2: Use the concept of remainders When a number is divided by 45 and leaves a remainder of 31, it means that the number is of the form 45n + 31, where n is the quotient.

Step 3: Find the remainder when divided by 15 We need to find the remainder when the number (45n + 31) is divided by 15.

We can break this down as follows: (45n divided by 15) + (31 divided by 15)

45n divided by 15 is just 3n, which leaves no remainder.

31 divided by 15 gives a quotient of 2 and a remainder of 1.

So, the remainder when the original number is divided by 15 is 1.