In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, then the dividend is

Options

A. 4236
B. 4306
C. 4336
D. 5336

Answer

To solve the problem step by step, we will use the relationships given in the question.

### Step 1: Identify the given values
We know:
- Remainder (R) = 46
- Divisor (D) = 10 times the quotient (Q)
- Divisor (D) = 5 times the remainder (R)

### Step 2: Express the divisor in terms of the remainder
From the information provided, we can express the divisor in terms of the remainder:
\[ D = 5R \]
Substituting the value of the remainder:
\[ D = 5 \times 46 \]
\[ D = 230 \]

### Step 3: Express the divisor in terms of the quotient
We also know that:
\[ D = 10Q \]
Now we can set the two expressions for the divisor equal to each other:
\[ 10Q = 230 \]

### Step 4: Solve for the quotient
Now, we can solve for Q:
\[ Q = \frac{230}{10} \]
\[ Q = 23 \]

### Step 5: Use the formula for the dividend
The formula for the dividend (D) in a division sum is:
\[ \text{Dividend} = D \times Q + R \]
Substituting the values we have:
\[ \text{Dividend} = 230 \times 23 + 46 \]

### Step 6: Calculate the dividend
Now we calculate the dividend:
\[ 230 \times 23 = 5290 \]
Now add the remainder:
\[ \text{Dividend} = 5290 + 46 \]
\[ \text{Dividend} = 5336 \]

### Final Answer
Thus, the dividend is **5336**.

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