Abhinav purchases a track suit for ₹ 2400 cash or for ₹ 1000 cash down payments and two monthly instalments of ₹ 800 each. Find the rate of interest:

Options

A. `75%`
B. `120%`
C. `50%`
D. none of these

Answer

To find the rate of interest for Abhinav's purchase of the track suit, we can follow these steps:

### Step 1: Identify the total cost of the track suit
The cash price of the track suit is ₹2400.

### Step 2: Identify the down payment and installments
Abhinav makes a down payment of ₹1000 and then pays two monthly installments of ₹800 each.

### Step 3: Calculate the total amount paid through installments
The total amount paid through installments is:
\[ \text{Total Installments} = 2 \times 800 = ₹1600 \]

### Step 4: Calculate the total amount paid
Now, we add the down payment to the total installments:
\[ \text{Total Amount Paid} = \text{Down Payment} + \text{Total Installments} = 1000 + 1600 = ₹2600 \]

### Step 5: Calculate the interest paid
The interest paid can be calculated by subtracting the cash price from the total amount paid:
\[ \text{Interest} = \text{Total Amount Paid} - \text{Cash Price} = 2600 - 2400 = ₹200 \]

### Step 6: Calculate the principal amount
The principal amount is the cash price minus the down payment:
\[ \text{Principal} = \text{Cash Price} - \text{Down Payment} = 2400 - 1000 = ₹1400 \]

### Step 7: Calculate the rate of interest
The rate of interest can be calculated using the formula:
\[ \text{Rate of Interest (R)} = \left( \frac{\text{Interest}}{\text{Principal}} \times \frac{100}{\text{Time}} \right) \]
Here, the time is 2 months (or \(\frac{2}{12}\) years):
\[ R = \left( \frac{200}{1400} \times \frac{100}{\frac{2}{12}} \right) \]

### Step 8: Simplify the calculation
First, calculate \(\frac{200}{1400}\):
\[ \frac{200}{1400} = \frac{1}{7} \]
Now, calculate \(\frac{100}{\frac{2}{12}} = 100 \times \frac{12}{2} = 600\):
\[ R = \left( \frac{1}{7} \times 600 \right) = \frac{600}{7} \approx 85.71\% \]

### Step 9: Conclusion
The rate of interest is approximately 85.71%. Since this is not one of the given options, we can round it to the nearest option, which is 90%.