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

Options

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

Answer

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

### Step 1: Understand the relationships
We know:
- The divisor (d) is 25 times the quotient (q).
- The divisor (d) is also 5 times the remainder (r).
- The quotient (q) is given as 16.

### Step 2: Express the divisor and remainder in terms of the quotient
From the information provided:
1. \( d = 25 \times q \)
2. \( d = 5 \times r \)

Since \( q = 16 \):
- Substitute \( q \) into the equation for the divisor:
\[ d = 25 \times 16 = 400 \]

### Step 3: Find the remainder
Now, using the divisor to find the remainder:
- From \( d = 5 \times r \):
\[ 400 = 5 \times r \]
- To find \( r \):
\[ r = \frac{400}{5} = 80 \]

### Step 4: Use the formula for the dividend
The formula for the dividend (D) is:
\[ D = d \times q + r \]
Substituting the values we have:
\[ D = 400 \times 16 + 80 \]

### Step 5: Calculate the dividend
Now, calculate \( D \):
1. Calculate \( 400 \times 16 \):
\[ 400 \times 16 = 6400 \]
2. Add the remainder:
\[ D = 6400 + 80 = 6480 \]

### Final Answer
The dividend is \( 6480 \).

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