When a number x is divided by a divisor it is seen that the divisor = 4 times the quotient = double the remainder. If the remainder is 80 then the value of x is

Options

A. 6480
B. 6980
C. 8460
D. 4680

Answer

To solve the problem step by step, we can follow these steps:

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

### Step 2: Set Up the Relationships
According to the problem:
1. The divisor \( d \) is 4 times the quotient \( y \):
\[ d = 4y \]
2. The divisor \( d \) is also double the remainder \( r \):
\[ d = 2r \]
3. We are given that the remainder \( r \) is 80:
\[ r = 80 \]

### Step 3: Substitute the Remainder
Substituting the value of \( r \) into the second equation:
\[ d = 2 \times 80 = 160 \]

### Step 4: Use the Divisor to Find the Quotient
Now, we can use the first equation to find \( y \):
\[ 160 = 4y \]
Solving for \( y \):
\[ y = \frac{160}{4} = 40 \]

### Step 5: Calculate the Value of \( x \)
Now we can find \( x \) using the formula:
\[ x = d \cdot y + r \]
Substituting the values we found:
\[ x = 160 \cdot 40 + 80 \]
Calculating:
\[ x = 6400 + 80 = 6480 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{6480} \]

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