The true discount on Rs. 1860 due 3 years hence is Rs. 60. Find the rate per cent-

Options

A. `10%`
B. `12%`
C. `5%`
D. `15%`

Answer

To find the rate percent given the true discount on Rs. 1860 due in 3 years is Rs. 60, we can follow these steps:

### Step 1: Understand the given values
- Amount (A) = Rs. 1860
- True Discount (TD) = Rs. 60
- Time (T) = 3 years

### Step 2: Calculate the Present Value (PV)
The Present Value can be calculated using the formula:
\[ PV = A - TD \]
Substituting the values:
\[ PV = 1860 - 60 = 1800 \]

### Step 3: Use the formula for True Discount to find the Rate
The formula for the rate (R) is:
\[ R = \frac{100 \times TD}{PV \times T} \]
Substituting the values we have:
\[ R = \frac{100 \times 60}{1800 \times 3} \]

### Step 4: Simplify the calculation
First, calculate the denominator:
\[ PV \times T = 1800 \times 3 = 5400 \]
Now substitute this back into the rate formula:
\[ R = \frac{6000}{5400} \]

### Step 5: Calculate the Rate
Now, simplify the fraction:
\[ R = \frac{6000 \div 600}{5400 \div 600} = \frac{10}{9} \]
To convert this to a percentage:
\[ R = \frac{10}{9} \times 100 \approx 111.11\% \]

### Final Answer
The rate percent is approximately **11.11%**.

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