A number when divided by 72 leaves remainder 10. What will be the remainder when the same number is divided by 9?

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem step by step, we start with the information given:

1. **Understanding the problem**: We know that a number \( x \) when divided by 72 leaves a remainder of 10. This can be expressed mathematically as:
\[ x = 72k + 10 \]
where \( k \) is some integer.

2. **Finding the remainder when divided by 9**: We need to find the remainder when \( x \) is divided by 9. To do this, we can substitute the expression for \( x \) into the equation and simplify:
\[ x = 72k + 10 \]

3. **Calculating \( 72 \mod 9 \)**: Next, we find the remainder of \( 72 \) when divided by \( 9 \):
\[ 72 \div 9 = 8 \quad \text{(exactly, with no remainder)} \]
Therefore, \( 72 \equiv 0 \mod 9 \).

4. **Calculating \( 10 \mod 9 \)**: Now we find the remainder of \( 10 \) when divided by \( 9 \):
\[ 10 \div 9 = 1 \quad \text{(with a remainder of 1)} \]
So, \( 10 \equiv 1 \mod 9 \).

5. **Combining the results**: Since \( 72k \equiv 0 \mod 9 \) and \( 10 \equiv 1 \mod 9 \), we can combine these results:
\[ x \equiv 0 + 1 \mod 9 \]
Thus,
\[ x \equiv 1 \mod 9 \]

6. **Conclusion**: The remainder when the number \( x \) is divided by \( 9 \) is \( 1 \).

### Final Answer:
The remainder when the same number is divided by 9 is **1**.