1.080 invested for 3 months gave an interest of 0.027. The simple rate of interest per annum was :
(a)`2.5 %`
(b)`5%`
(c)`7.5%`
(d)`10%`

Options

A. `2.5 %`
B. `5%`
C. `7.5%`
D. `10%`

Answer

To find the simple rate of interest per annum, we can use the formula for simple interest:

\[ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \]

Where:
- \( P \) = Principal amount (the initial amount of money)
- \( R \) = Rate of interest per annum
- \( T \) = Time (in years)

Given:
- Principal \( P = 1.080 \)
- Simple Interest \( SI = 0.027 \)
- Time \( T = 3 \text{ months} = \frac{3}{12} \text{ years} = \frac{1}{4} \text{ years} \)

### Step 1: Substitute the known values into the formula

We can rearrange the formula to solve for \( R \):

\[ R = \frac{SI \times 100}{P \times T} \]

Substituting the known values:

\[ R = \frac{0.027 \times 100}{1.080 \times \frac{1}{4}} \]

### Step 2: Calculate the denominator

First, calculate \( 1.080 \times \frac{1}{4} \):

\[ 1.080 \times \frac{1}{4} = \frac{1.080}{4} = 0.270 \]

### Step 3: Substitute back into the equation for \( R \)

Now substitute \( 0.270 \) back into the equation for \( R \):

\[ R = \frac{0.027 \times 100}{0.270} \]

### Step 4: Calculate the numerator

Calculate \( 0.027 \times 100 \):

\[ 0.027 \times 100 = 2.7 \]

### Step 5: Calculate \( R \)

Now substitute this value into the equation:

\[ R = \frac{2.7}{0.270} \]

Calculating this gives:

\[ R = 10 \]

### Conclusion

Thus, the simple rate of interest per annum is:

\[ \text{Rate} = 10\% \]

The correct answer is (d) 10%.

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