The true discount on Rs. 340 due 5 years hence is Rs. 40. Find the rate per cent-

Options

A. `3%`
B. `2 2/3%`
C. `3 1/3%`
D. `3 2/3%`

Answer

To solve the problem step by step, we will use the concept of true discount and the formula for calculating the rate of interest.

### Step 1: Understand the given values
- Amount (A) = Rs. 340
- True Discount (TD) = Rs. 40
- Time (t) = 5 years

### Step 2: Calculate the Present Worth (PW)
The Present Worth (PW) can be calculated using the formula:
\[ \text{PW} = \text{Amount} - \text{True Discount} \]

Substituting the values:
\[ \text{PW} = 340 - 40 = 300 \]

### Step 3: Use the formula to find the rate of interest
The formula for calculating the rate (R) is:
\[ R = \frac{100 \times \text{True Discount}}{\text{Present Worth} \times t} \]

Substituting the values:
\[ R = \frac{100 \times 40}{300 \times 5} \]

### Step 4: Simplify the equation
Calculating the denominator:
\[ 300 \times 5 = 1500 \]

Now substituting back into the formula:
\[ R = \frac{4000}{1500} \]

### Step 5: Further simplify the fraction
\[ R = \frac{4000 \div 500}{1500 \div 500} = \frac{8}{3} \]

### Step 6: Convert the fraction to a percentage
To convert \( \frac{8}{3} \) into a mixed number:
\[ \frac{8}{3} = 2 \frac{2}{3} \]

### Final Answer
The rate of interest is \( 2 \frac{2}{3} \% \).

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