What rate per cent does Shantanu get for his money when in discounting a bill due 30 months hence he deducts 30% of the amount of the bill ?

Options

A. `17(2)/(7)%`
B. `17(3)/(7)%`
C. `17(5)/(7)%`
D. `17(1)/(7)%`

Answer

To solve the problem, we need to determine the rate of interest Shantanu receives when he discounts a bill due in 30 months by deducting 30% of its value. Here’s a step-by-step breakdown of the solution:

### Step 1: Define the Value of the Bill
Let’s assume the value of the bill is Rs. 100.

### Step 2: Calculate the Discount Amount
Shantanu deducts 30% of the bill amount.
- Discount = 30% of 100 = \( \frac{30}{100} \times 100 = 30 \) Rs.

### Step 3: Calculate the Amount Received by the Holder of the Bill
The amount the holder of the bill receives after the discount is:
- Amount received = Bill amount - Discount = \( 100 - 30 = 70 \) Rs.

### Step 4: Calculate the Simple Interest for 30 Months
The simple interest on the amount received (Rs. 70) for 30 months needs to be calculated. Since the interest is typically calculated annually, we need to convert the time period:
- Simple Interest (SI) = Amount received × Rate × Time
- Here, we will find the interest for 30 months.

### Step 5: Calculate the Total Simple Interest
For 30 months, the simple interest can be calculated as:
- SI = Principal × Rate × Time
- SI = 70 × Rate × \( \frac{30}{12} \) (since 30 months is \( \frac{30}{12} \) years)

### Step 6: Set Up the Equation
We know that the total simple interest earned is equal to the discount amount:
- \( 30 = 70 \times \text{Rate} \times \frac{30}{12} \)

### Step 7: Solve for the Rate
Rearranging the equation to find the rate:
- \( \text{Rate} = \frac{30 \times 12}{70 \times 30} \)
- Simplifying gives us:
- \( \text{Rate} = \frac{12}{70} \)
- \( \text{Rate} = \frac{6}{35} \)

### Step 8: Convert to Percentage
To convert the rate into percentage:
- \( \text{Rate Percentage} = \frac{6}{35} \times 100 \)

### Step 9: Simplify the Calculation
Calculating \( \frac{600}{35} \):
- \( \text{Rate Percentage} = 17.14 \) (approximately)
- This can also be expressed as \( 17 \frac{1}{7} \% \).

### Final Answer
Thus, the rate per cent that Shantanu gets for his money is approximately **17 \( \frac{1}{7} \% \)**.

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