A sum of money (P) doubles in 10 years. How much would it be in 20 years at the same rate of simple interest?
A.P
B. 2P
C. 3P
D. 4P

Options

A. D
B. C
C. B
D. A

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Problem
We know that a sum of money (P) doubles in 10 years under simple interest. We need to find out how much this sum will be in 20 years at the same rate of simple interest.

### Step 2: Use the Simple Interest Formula
The formula for calculating simple interest (SI) is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 3: Determine the Interest for 10 Years
Since the amount doubles in 10 years, we can express this as:
\[ \text{Amount} = P + \text{SI} = 2P \]
This implies:
\[ \text{SI} = 2P - P = P \]
So, the interest earned in 10 years is \( P \).

### Step 4: Calculate the Rate of Interest
Using the simple interest formula for the first 10 years:
\[ P = \frac{P \times R \times 10}{100} \]
From this, we can solve for \( R \):
\[ P = \frac{10PR}{100} \]
\[ 100 = 10R \]
\[ R = 10\% \]

### Step 5: Calculate the Interest for 20 Years
Now, we need to find the interest for 20 years at the same rate of interest (10%):
Using the simple interest formula again:
\[ \text{SI}_{20} = \frac{P \times 10 \times 20}{100} \]
\[ \text{SI}_{20} = \frac{P \times 200}{100} = 2P \]

### Step 6: Calculate the Total Amount After 20 Years
Now, we can find the total amount after 20 years:
\[ \text{Amount}_{20} = P + \text{SI}_{20} \]
\[ \text{Amount}_{20} = P + 2P = 3P \]

### Final Answer
Thus, the amount after 20 years will be \( 3P \).

### Options
The correct answer is **C. 3P**.

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