A divisor is 25 times the quotient and 5 times the remainder. The quotient is 16, the dividend is

Options

A. 6400
B. 6480
C. 400
D. 480

Answer

To solve the problem step by step, let's break down the information given and apply it systematically.

### Step 1: Define the variables
Let:
- \( D \) = Divisor
- \( Q \) = Quotient
- \( R \) = Remainder

From the problem, we know:
- \( Q = 16 \) (given)
- \( D = 25 \times Q \)
- \( D = 5 \times R \)

### Step 2: Calculate the Divisor
Using the value of the quotient:
\[ D = 25 \times Q = 25 \times 16 = 400 \]
So, the divisor \( D \) is 400.

### Step 3: Relate Divisor and Remainder
We also know from the problem that:
\[ D = 5 \times R \]
Substituting the value of \( D \):
\[ 400 = 5 \times R \]

### Step 4: Solve for the Remainder
Now, we can solve for \( R \):
\[ R = \frac{400}{5} = 80 \]
So, the remainder \( R \) is 80.

### Step 5: Calculate the Dividend
The formula for the dividend \( Dv \) is:
\[ Dv = D \times Q + R \]
Substituting the values we have:
\[ Dv = 400 \times 16 + 80 \]
Calculating this:
\[ Dv = 6400 + 80 = 6480 \]

### Conclusion
Thus, the dividend is \( 6480 \).

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