The divisior is 50 times the quotient and 10 times the remainder. If the quotient is 32, what is the dividend?

Options

A. 51000
B. 51360
C. 61000
D. 61520

Answer

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

### Step 1: Define the Variables
Let:
- \( D \) = Dividend
- \( d \) = Divisor
- \( q \) = Quotient
- \( r \) = Remainder

From the question, we know:
- The quotient \( q = 32 \)

### Step 2: Establish Relationships
According to the problem:
1. The divisor \( d \) is 50 times the quotient:
\[ d = 50 \times q \]
2. The divisor \( d \) is also 10 times the remainder:
\[ d = 10 \times r \]

### Step 3: Calculate the Divisor
Substituting the value of \( q \) into the first equation:
\[ d = 50 \times 32 = 1600 \]

### Step 4: Calculate the Remainder
Using the second equation to find the remainder:
\[ d = 10 \times r \implies 1600 = 10 \times r \implies r = \frac{1600}{10} = 160 \]

### Step 5: Calculate the Dividend
Now, we can use the formula for the dividend:
\[ D = d \times q + r \]
Substituting the values we found:
\[ D = 1600 \times 32 + 160 \]

Calculating \( 1600 \times 32 \):
\[ 1600 \times 32 = 51200 \]

Now, adding the remainder:
\[ D = 51200 + 160 = 51360 \]

### Final Answer
The dividend \( D \) is:
\[ \boxed{51360} \]