In a division sum, the divisor is 5 times the quotient and twice the remainder. If the remainder is 5, what is the dividend?

Options

A. 52
B. 15
C. 25
D. 48

Answer

To solve the problem step by step, we will follow the relationships between the divisor, quotient, remainder, and dividend.

### Step-by-Step Solution:

1. **Understand the relationships**:
- In a division, the relationship between the dividend (D), divisor (d), quotient (q), and remainder (r) is given by the formula:
\[ D = d \times q + r \]

2. **Identify the given values**:
- We know that the remainder \( r = 5 \).
- The problem states that the divisor \( d \) is 5 times the quotient \( q \) and also twice the remainder \( r \).

3. **Express the divisor in terms of the remainder**:
- Since \( d \) is twice the remainder:
\[ d = 2 \times r \]
- Substituting the value of the remainder:
\[ d = 2 \times 5 = 10 \]

4. **Express the divisor in terms of the quotient**:
- Since \( d \) is also 5 times the quotient:
\[ d = 5 \times q \]
- We already found that \( d = 10 \), so we can set up the equation:
\[ 10 = 5 \times q \]

5. **Solve for the quotient**:
- To find \( q \), divide both sides by 5:
\[ q = \frac{10}{5} = 2 \]

6. **Calculate the dividend**:
- Now that we have \( d \) and \( q \), we can use the formula for the dividend:
\[ D = d \times q + r \]
- Substitute the known values:
\[ D = 10 \times 2 + 5 \]
- Calculate:
\[ D = 20 + 5 = 25 \]

7. **Final answer**:
- The dividend is \( 25 \).

### Summary:
The dividend in the division sum is \( 25 \).