Any amount gets triple in 15 years 6 months, then in how much time will it be double?

Options

A. 6 years 9 months
B. 7 years 9 months
C. 8 years 3 months
D. 9 year 6 months

Answer

To solve the problem of how long it will take for an amount to double when it triples in 15 years and 6 months, we can use the concept of simple interest. Here’s a step-by-step solution:

### Step 1: Understand the given information
We know that an amount triples in 15 years and 6 months. This means that if we start with an amount \( P \), after 15 years and 6 months, the amount becomes \( 3P \).

### Step 2: Convert the time into a single unit
Convert 15 years and 6 months into years:
\[ 15 \text{ years} + 6 \text{ months} = 15 + \frac{6}{12} = 15.5 \text{ years} \]

### Step 3: Set up the relationship using simple interest
Using the formula for simple interest, we can express the relationship as:
\[ \frac{n_1 - 1}{t_1} = \frac{n_2 - 1}{t_2} \]
Where:
- \( n_1 = 3 \) (the amount becomes triple)
- \( t_1 = 15.5 \) years (the time it takes to triple)
- \( n_2 = 2 \) (the amount becomes double)
- \( t_2 \) is the time we want to find.

### Step 4: Substitute the values into the equation
Substituting the known values into the equation:
\[ \frac{3 - 1}{15.5} = \frac{2 - 1}{t_2} \]
This simplifies to:
\[ \frac{2}{15.5} = \frac{1}{t_2} \]

### Step 5: Cross-multiply to solve for \( t_2 \)
Cross-multiplying gives:
\[ 2t_2 = 15.5 \]
Thus,
\[ t_2 = \frac{15.5}{2} = 7.75 \text{ years} \]

### Step 6: Convert \( t_2 \) into years and months
To convert 7.75 years into years and months:
- The whole number part is 7 years.
- The decimal part \( 0.75 \) of a year can be converted to months:
\[ 0.75 \times 12 = 9 \text{ months} \]
So, \( t_2 = 7 \text{ years and } 9 \text{ months} \).

### Final Answer
The time it will take for the amount to double is **7 years and 9 months**.

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