In a problem involving division, the divisor is eight times the quotient and four times the remainder. If the remainder is 12, then the dividend is :

Options

A. 300
B. 288
C. 512
D. 524

Answer

To solve the problem step by step, we will break down the information provided and use it to find the dividend.

### Step 1: Understand the relationships
We know from the problem that:
- The divisor (D) is 8 times the quotient (Q).
- The divisor (D) is also 4 times the remainder (R).
- The remainder (R) is given as 12.

### Step 2: Calculate the divisor
Since the remainder is 12, we can find the divisor using the relationship that the divisor is 4 times the remainder:
\[ D = 4 \times R \]
Substituting the value of R:
\[ D = 4 \times 12 = 48 \]

### Step 3: Calculate the quotient
Now that we have the divisor, we can find the quotient using the relationship that the divisor is 8 times the quotient:
\[ D = 8 \times Q \]
Substituting the value of D:
\[ 48 = 8 \times Q \]
To find Q, we divide both sides by 8:
\[ Q = \frac{48}{8} = 6 \]

### Step 4: Calculate the dividend
The formula for the dividend (Div) in terms of the divisor, quotient, and remainder is:
\[ \text{Dividend} = D \times Q + R \]
Substituting the values we found:
\[ \text{Dividend} = 48 \times 6 + 12 \]
Calculating this gives:
\[ \text{Dividend} = 288 + 12 = 300 \]

### Conclusion
Thus, the dividend is **300**.

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