In a division sum, the divisor is 12 times the quotient and 5 times the remainder. If the remainder is 36, then the dividend is

Options

A. 2706
B. 2796
C. 2736
D. 2826

Answer

To solve the problem step by step, we will use the information given in the question regarding the divisor, quotient, and remainder.

### Step 1: Define the variables
Let:
- \( q \) = quotient
- \( r \) = remainder
- \( d \) = divisor
- \( D \) = dividend

From the problem, we know:
- The remainder \( r = 36 \).

### Step 2: Express the divisor in terms of the quotient
According to the problem:
- The divisor \( d \) is 12 times the quotient:
\[ d = 12q \]

### Step 3: Express the divisor in terms of the remainder
We also know that:
- The divisor \( d \) is 5 times the remainder:
\[ d = 5r \]

### Step 4: Substitute the value of the remainder
Since we know \( r = 36 \), we can substitute this into the equation for the divisor:
\[ d = 5 \times 36 = 180 \]

### Step 5: Set the two expressions for the divisor equal to each other
Now we have two expressions for the divisor:
\[ 12q = 180 \]

### Step 6: Solve for the quotient
To find \( q \), we can rearrange the equation:
\[ q = \frac{180}{12} = 15 \]

### Step 7: Use the division algorithm to find the dividend
The formula for the dividend is given by:
\[ D = d \times q + r \]
Substituting the known values:
\[ D = 180 \times 15 + 36 \]

### Step 8: Calculate the dividend
Now, we perform the multiplication and addition:
\[ D = 2700 + 36 = 2736 \]

### Final Answer
Thus, the dividend \( D \) is:
\[ \boxed{2736} \]