In a question on division, the divisor is 7 times the quotient and 3 times the remainder. If the remainder is 28, then the dividend is

Options

A. 588
B. 784
C. 823
D. 1036

Answer

To solve the problem, we need to find the dividend given that the divisor is 7 times the quotient and 3 times the remainder, with the remainder being 28.

### Step-by-Step Solution:

1. **Identify the given values:**
- Remainder (R) = 28

2. **Express the divisor (D) in terms of the quotient (Q):**
- According to the problem, the divisor is 3 times the remainder:
\[ D = 3R \]
- Substituting the value of R:
\[ D = 3 \times 28 = 84 \]

3. **Express the divisor (D) in terms of the quotient (Q):**
- The problem states that the divisor is also 7 times the quotient:
\[ D = 7Q \]
- We already found that D = 84, so we can set up the equation:
\[ 84 = 7Q \]

4. **Solve for the quotient (Q):**
- Divide both sides by 7:
\[ Q = \frac{84}{7} = 12 \]

5. **Use the formula for the dividend (N):**
- The formula for the dividend is:
\[ N = D \times Q + R \]
- Substitute the values of D, Q, and R:
\[ N = 84 \times 12 + 28 \]

6. **Calculate the dividend (N):**
- First, calculate \( 84 \times 12 \):
\[ 84 \times 12 = 1008 \]
- Now add the remainder:
\[ N = 1008 + 28 = 1036 \]

7. **Final answer:**
- The dividend is:
\[ \boxed{1036} \]