If the interest on Rs. 1200 be more than the interest on Rs. 1000 by Rs. 50 in 3 years, the rate per cent is

Options

A. `10 1/3%`
B. `6 2/3%`
C. `8 1/3%`
D. `9 2/3%`

Answer

To solve the problem step by step, we need to find the rate of interest (R) given that the interest on Rs. 1200 is more than the interest on Rs. 1000 by Rs. 50 in 3 years.

### Step 1: Understand the formula for Simple Interest
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 2: Set up the equations for both principal amounts
Let’s denote:
- \( SI_1 \) as the interest on Rs. 1200
- \( SI_2 \) as the interest on Rs. 1000

From the problem, we know:
\[ SI_1 - SI_2 = 50 \]

Now, using the formula for Simple Interest:
\[ SI_1 = \frac{1200 \times R \times 3}{100} \]
\[ SI_2 = \frac{1000 \times R \times 3}{100} \]

### Step 3: Substitute the values into the equation
Substituting \( SI_1 \) and \( SI_2 \) into the equation:
\[ \frac{1200 \times R \times 3}{100} - \frac{1000 \times R \times 3}{100} = 50 \]

### Step 4: Simplify the equation
We can simplify the equation:
\[ \frac{3R}{100} (1200 - 1000) = 50 \]
\[ \frac{3R}{100} \times 200 = 50 \]

### Step 5: Further simplify
Now, simplifying further:
\[ \frac{600R}{100} = 50 \]
\[ 6R = 50 \]

### Step 6: Solve for R
Now, divide both sides by 6:
\[ R = \frac{50}{6} = \frac{25}{3} \]

### Step 7: Convert to percentage
To express \( R \) as a percentage:
\[ R = 8 \frac{1}{3} \text{ percent} \]

### Final Answer
Thus, the rate of interest is:
\[ \boxed{8 \frac{1}{3} \text{ percent}} \]

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