A certain sum of money triple itself in 8 years. In how many years it will be five times?

Options

A. 22 years
B. 16 years
C. 20 years
D. 24 years

Answer

To solve the problem step by step, we will use the concept of simple interest.

### Step 1: Understand the Problem
We know that a certain sum of money triples itself in 8 years. We need to find out how many years it will take for the same sum to become five times.

### Step 2: Define Variables
Let:
- \( P \) = Principal amount (initial sum of money)
- \( I \) = Interest earned
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 3: Calculate Interest Earned in 8 Years
If the money triples in 8 years, then:
- After 8 years, the total amount \( A = 3P \)
- The interest earned \( I \) can be calculated as:
\[ I = A - P = 3P - P = 2P \]

### Step 4: Use the Simple Interest Formula
The formula for simple interest is:
\[ I = \frac{P \times R \times T}{100} \]
Substituting the values we have:
\[ 2P = \frac{P \times R \times 8}{100} \]

### Step 5: Simplify the Equation
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 2 = \frac{R \times 8}{100} \]
Now, multiply both sides by 100:
\[ 200 = R \times 8 \]
Now, divide by 8:
\[ R = 25\% \]

### Step 6: Calculate Time for the Amount to Become Five Times
Now we need to find out how long it will take for the amount to become five times:
- Total amount when it becomes five times \( A = 5P \)
- The interest earned in this case will be:
\[ I = A - P = 5P - P = 4P \]

### Step 7: Set Up the Equation for Simple Interest
Using the simple interest formula again:
\[ 4P = \frac{P \times R \times T}{100} \]
Substituting \( R = 25 \):
\[ 4P = \frac{P \times 25 \times T}{100} \]

### Step 8: Simplify the Equation Again
Cancel \( P \) from both sides:
\[ 4 = \frac{25T}{100} \]
Multiply both sides by 100:
\[ 400 = 25T \]
Now divide by 25:
\[ T = 16 \]

### Conclusion
It will take **16 years** for the sum of money to become five times.

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