Find the time in which the simple interest on a sum of money will be `(4)/(5)` times the principal at `8%` per anuum.

Answer

To find the time in which the simple interest on a sum of money will be \(\frac{4}{5}\) times the principal at an interest rate of \(8\%\) per annum, we can follow these steps:

### Step 1: Define the variables
Let:
- \(P\) = Principal amount
- \(r\) = Rate of interest = \(8\%\)
- \(t\) = Time in years
- Simple Interest (SI) = \(\frac{4}{5}P\)

### Step 2: Write the formula for Simple Interest
The formula for Simple Interest is given by:
\[ SI = \frac{P \times r \times t}{100} \]

### Step 3: Set up the equation
According to the problem, the Simple Interest is \(\frac{4}{5}P\). Therefore, we can set up the equation:
\[ \frac{4}{5}P = \frac{P \times 8 \times t}{100} \]

### Step 4: Cancel \(P\) from both sides
Since \(P\) is a common factor on both sides (assuming \(P \neq 0\)), we can cancel it:
\[ \frac{4}{5} = \frac{8t}{100} \]

### Step 5: Cross-multiply to solve for \(t\)
Cross-multiplying gives us:
\[ 4 \times 100 = 5 \times 8t \]
\[ 400 = 40t \]

### Step 6: Solve for \(t\)
Now, divide both sides by \(40\):
\[ t = \frac{400}{40} = 10 \]

### Final Answer
The time \(t\) is \(10\) years.

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