A cellphone is available for ₹ 600 or for 300 cash down payment together with ₹ 360 to be paid after two months. Find the rate of interest charged under this scheme :

Options

A. `20%`
B. `50%`
C. `120%`
D. none of these

Answer

To find the rate of interest charged under the given installment scheme for the cellphone, we can follow these steps:

### Step 1: Understand the Payment Options
The cellphone is available for:
- Cash price: ₹600
- Installment option: ₹300 down payment + ₹360 after 2 months

### Step 2: Calculate Total Payment in Installment Option
Total payment if taken on installment:
- Down payment: ₹300
- Payment after 2 months: ₹360
- Total payment = ₹300 + ₹360 = ₹660

### Step 3: Calculate the Extra Amount Paid
Now, we need to find how much extra is paid when opting for the installment plan compared to the cash price.
- Extra amount paid = Total payment on installment - Cash price
- Extra amount = ₹660 - ₹600 = ₹60

### Step 4: Determine the Principal Amount
The principal amount (the amount on which interest is calculated) is the remaining amount after the down payment.
- Principal = Cash price - Down payment
- Principal = ₹600 - ₹300 = ₹300

### Step 5: Calculate the Rate of Interest
We can use the formula for simple interest to find the rate of interest:
\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]
Where:
- Interest = ₹60
- Principal = ₹300
- Time = 2 months = \( \frac{2}{12} \) years = \( \frac{1}{6} \) years

Rearranging the formula to find the rate (R):
\[ R = \frac{\text{Interest}}{\text{Principal} \times \text{Time}} \]

Substituting the values:
\[ R = \frac{60}{300 \times \frac{1}{6}} \]

### Step 6: Simplify the Calculation
Calculating the denominator:
\[ 300 \times \frac{1}{6} = 50 \]

Now substituting back into the formula:
\[ R = \frac{60}{50} = 1.2 \]

### Step 7: Convert to Percentage
To convert the rate into a percentage, multiply by 100:
\[ R = 1.2 \times 100 = 120\% \]

### Conclusion
The rate of interest charged under this scheme is **120%**.

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