Find the divisor given that the dividend is 2200 remainder is 13 the divisor is one third of the quotient

Options

A. 25
B. 27
C. 24
D. none of these

Explanation

To find the divisor given the dividend, remainder, and the relationship between the divisor and the quotient, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Dividend (D) = 2200
- Remainder (R) = 13
- Let the Quotient (Q) = x
- Since the divisor (d) is one-third of the quotient, we have:
\[ d = \frac{x}{3} \]

2. **Use the Dividend Formula**:
The relationship between dividend, divisor, quotient, and remainder is given by:
\[ D = Q \times d + R \]
Substituting the known values:
\[ 2200 = x \times \frac{x}{3} + 13 \]

3. **Rearrange the Equation**:
First, subtract the remainder from both sides:
\[ 2200 - 13 = \frac{x^2}{3} \]
This simplifies to:
\[ 2187 = \frac{x^2}{3} \]

4. **Multiply by 3 to Eliminate the Fraction**:
Multiply both sides by 3:
\[ 2187 \times 3 = x^2 \]
This gives:
\[ 6561 = x^2 \]

5. **Take the Square Root**:
To find x, take the square root of both sides:
\[ x = \sqrt{6561} \]
Calculating the square root gives:
\[ x = 81 \]

6. **Find the Divisor**:
Now that we have the quotient (x), we can find the divisor:
\[ d = \frac{x}{3} = \frac{81}{3} = 27 \]

### Final Answer:
The divisor is **27**.