Rs 1,000 is inverset at 5 % per annum simpe interset. If the interset is added to the principal after how many year, the amount will become Rs 2,000 after

Options

A. (a) 15 yeas
B. (b)18 years
C. (c)20 years
D. (d)16 2/3 years

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI) and the relationship between Principal (P), Interest (I), and Amount (A).

### Given:
- Principal (P) = Rs 1,000
- Rate of Interest (R) = 5% per annum
- Amount (A) = Rs 2,000

### Step 1: Find the Total Interest Earned
The total interest earned can be calculated using the formula:
\[ A = P + I \]
Where:
- \( I \) is the interest earned.

Rearranging the formula gives:
\[ I = A - P \]
Substituting the values:
\[ I = 2000 - 1000 = 1000 \]

### Step 2: Use the Simple Interest Formula
The formula for Simple Interest is:
\[ I = \frac{P \times R \times T}{100} \]
Where:
- \( T \) is the time in years.

We can rearrange this formula to solve for \( T \):
\[ T = \frac{I \times 100}{P \times R} \]

### Step 3: Substitute the Values
Now, substitute the values of \( I \), \( P \), and \( R \) into the formula:
\[ T = \frac{1000 \times 100}{1000 \times 5} \]

### Step 4: Simplify the Expression
Calculating the right-hand side:
\[ T = \frac{100000}{5000} \]
\[ T = 20 \]

### Conclusion
The time required for the amount to become Rs 2,000 is **20 years**.

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