If amount of Rs 21000 becomes 30000 in certain time period with rate of interest 10% then find the time period?

Options

A. `4(7)/(3)` year
B. `4(2)/(7)` year
C. `3(4)/(7)` year
D. `4(3)/(7)` year

Answer

To solve the problem step by step, we need to find the time period for which the principal amount of Rs 21,000 becomes Rs 30,000 at a rate of interest of 10%.

### Step 1: Identify the given values
- Principal (P) = Rs 21,000
- Amount (A) = Rs 30,000
- Rate of Interest (R) = 10%

### Step 2: Calculate the Simple Interest (SI)
The formula for Simple Interest is:
\[ \text{SI} = \text{Amount} - \text{Principal} \]
Substituting the values:
\[ \text{SI} = 30,000 - 21,000 = 9,000 \]

### Step 3: Use the Simple Interest formula to find Time (T)
The formula for Simple Interest is also given by:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
We can rearrange this formula to solve for time (T):
\[ T = \frac{\text{SI} \times 100}{P \times R} \]

### Step 4: Substitute the values into the formula
Now, substituting the values we have:
\[ T = \frac{9,000 \times 100}{21,000 \times 10} \]

### Step 5: Simplify the expression
Calculating the denominator:
\[ 21,000 \times 10 = 210,000 \]
Now substituting this back into the equation for T:
\[ T = \frac{900,000}{210,000} \]

### Step 6: Perform the division
\[ T = \frac{900,000 \div 210,000} = \frac{900}{210} \]
Now simplifying:
\[ T = \frac{90}{21} \approx 4.2857 \]

### Step 7: Convert to years
Since the interest rate is typically annual, we can round this to:
\[ T \approx 4.29 \text{ years} \]
Thus, the time period is approximately 4.29 years.

### Final Answer
The time period is approximately **4.29 years**.

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