Mayank invested Rs 17500 in ascheme P which offered simple interest at the rate of R% for two years. After two years he withdrew the principal amount plus interest and invested the entire amount in another scheme Q. Which offers simple interest at the rate of 20% for two years. If he got total interest of Rs 8680 after two years. Find value of R?

Options

A. `10%`
B. `15%`
C. `12%`
D. `20%`

Answer

To solve the problem step-by-step, we will follow the process of calculating the simple interest for both schemes and then find the value of R.

### Step 1: Calculate the Simple Interest for Scheme P
The formula for Simple Interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest
- \( T \) = Time in years

For Scheme P:
- Principal amount \( P = 17500 \)
- Rate of interest \( R = R\% \)
- Time \( T = 2 \) years

Thus, the Simple Interest for Scheme P is:
\[ SI_P = \frac{17500 \times R \times 2}{100} = \frac{35000R}{100} = 350R \]

### Step 2: Total Amount Withdrawn from Scheme P
After 2 years, the total amount withdrawn from Scheme P (Principal + Interest) is:
\[ A_P = P + SI_P = 17500 + 350R \]

### Step 3: Calculate the Simple Interest for Scheme Q
For Scheme Q:
- The total amount invested is \( A_P = 17500 + 350R \)
- Rate of interest = 20%
- Time = 2 years

The Simple Interest for Scheme Q is:
\[ SI_Q = \frac{(17500 + 350R) \times 20 \times 2}{100} = \frac{(17500 + 350R) \times 40}{100} = \frac{(17500 + 350R) \times 40}{100} = 4400 + 140R \]

### Step 4: Set Up the Equation
According to the problem, the total interest earned after 2 years in Scheme Q is Rs 8680. Thus, we can set up the equation:
\[ 4400 + 140R = 8680 \]

### Step 5: Solve for R
Now, we will solve for \( R \):
1. Subtract 4400 from both sides:
\[ 140R = 8680 - 4400 \]
\[ 140R = 4280 \]

2. Divide both sides by 140:
\[ R = \frac{4280}{140} \]
\[ R = 30.5714 \approx 30.57 \]

### Step 6: Final Calculation
To find the exact value of R, we can simplify:
\[ R = \frac{4280}{140} = 30.57 \]

### Step 7: Check Options
The options given were 10%, 15%, 12%, and 20%. Since none of these match, we can conclude that there might be a mistake in the options provided.