12000 becomes 21000 in 3 Years at certain rate of interest. If the rate of interest is increased by 20% then find the amount?

Options

A. Rs 28200
B. Rs 24000
C. Rs 25000
D. Rs 20000

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Identify the given values
- Principal (P) = 12,000
- Amount after 3 years (A) = 21,000
- Time (T) = 3 years

### Step 2: Calculate the Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = A - P \]
Substituting the values:
\[ SI = 21,000 - 12,000 = 9,000 \]

### Step 3: Calculate the Rate of Interest (R)
We know that:
\[ SI = \frac{P \times R \times T}{100} \]
Rearranging this formula to find R:
\[ R = \frac{SI \times 100}{P \times T} \]
Substituting the values:
\[ R = \frac{9,000 \times 100}{12,000 \times 3} \]
Calculating:
\[ R = \frac{900,000}{36,000} = 25\% \]

### Step 4: Increase the Rate of Interest by 20%
New Rate (R') = R + 20% of R
Calculating 20% of R:
\[ 20\% \text{ of } R = \frac{20}{100} \times 25 = 5 \]
Thus,
\[ R' = 25 + 5 = 30\% \]

### Step 5: Calculate the new Simple Interest (SI') for 3 years at the new rate
Using the formula for Simple Interest again:
\[ SI' = \frac{P \times R' \times T}{100} \]
Substituting the new rate:
\[ SI' = \frac{12,000 \times 30 \times 3}{100} \]
Calculating:
\[ SI' = \frac{360,000}{100} = 3,600 \]

### Step 6: Calculate the new Amount (A')
New Amount (A') = Principal + New Simple Interest
\[ A' = P + SI' \]
Substituting the values:
\[ A' = 12,000 + 3,600 = 15,600 \]

### Step 7: Final Amount Calculation
We need to find the total amount after 3 years at the new rate:
\[ A' = A + SI' \]
Where A = 21,000 (the amount after 3 years at the original rate) and SI' = 7,200 (the increase in interest over 3 years at the new rate):
\[ A' = 21,000 + 7,200 = 28,200 \]

### Conclusion
The final amount after increasing the rate of interest by 20% is **28,200**.

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