In a division sum, the divisor'd is 10 times the quotient'd and 5 times the remainder 'Y. If r= 46, then the dividend will be

Options

A. 5042
B. 5328
C. 5336
D. 4276

Answer

To solve the problem, we need to use the relationships given in the question regarding the divisor, quotient, and remainder. Let's break it down step by step.

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

From the problem, we know:
- \( d = 10q \) (the divisor is 10 times the quotient)
- \( d = 5r \) (the divisor is 5 times the remainder)

### Step 2: Substitute the value of the remainder
We are given that \( r = 46 \).

Using this value, we can substitute into the equation for the divisor:
\[ d = 5r = 5 \times 46 = 230 \]

### Step 3: Find the quotient
Now that we have the divisor \( d \), we can use the relationship \( d = 10q \) to find \( q \):
\[ 230 = 10q \]
Dividing both sides by 10 gives:
\[ q = \frac{230}{10} = 23 \]

### Step 4: Calculate the dividend
The formula for the dividend \( p \) in a division sum is given by:
\[ p = dq + r \]
Substituting the values we have:
\[ p = 230 \times 23 + 46 \]

### Step 5: Perform the multiplication
Calculating \( 230 \times 23 \):
\[ 230 \times 23 = 5290 \]

### Step 6: Add the remainder
Now, add the remainder:
\[ p = 5290 + 46 = 5336 \]

### Final Answer
Thus, the dividend is:
\[ \boxed{5336} \]