A mobile is sold for Rs 4400 cash or for Rs 2000 cash down payment together with Rs 2440 to be paid after one month. Find the rate of interest changed in the installment scheme.

Options

A. `20%`
B. `18%`
C. `15%`
D. `19%`

Answer

To solve the problem, we need to find the rate of interest charged in the installment scheme for the mobile phone.

### Step-by-Step Solution:

1. **Identify the Cash Price and Installment Payment**:
- The cash price of the mobile is Rs 4400.
- In the installment scheme, the customer pays Rs 2000 as a down payment and Rs 2440 after one month.

2. **Calculate the Total Amount Paid in Installment**:
- Total amount paid = Down payment + Amount paid after one month
- Total amount paid = Rs 2000 + Rs 2440 = Rs 4440.

3. **Determine the Extra Amount Paid**:
- Extra amount paid in the installment scheme = Total amount paid - Cash price
- Extra amount paid = Rs 4440 - Rs 4400 = Rs 40.

4. **Calculate the Principal Amount**:
- The principal amount (P) is the remaining amount after the down payment.
- Principal amount = Rs 2440 (the amount paid after one month).

5. **Calculate the Time Period**:
- The time period (T) for which the interest is calculated is 1 month, which can be expressed in years as:
- T = 1 month = 1/12 years.

6. **Use the Simple Interest Formula**:
- The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
- Here, SI is the extra amount paid (Rs 40), P is the principal (Rs 2440), and T is 1/12 years.
- We need to find the rate of interest (R).

7. **Substituting the Values**:
- Substitute the known values into the formula:
\[ 40 = \frac{2440 \times R \times \frac{1}{12}}{100} \]

8. **Rearranging the Equation**:
- Multiply both sides by 100 to eliminate the fraction:
\[ 4000 = 2440 \times R \times \frac{1}{12} \]
- Multiply both sides by 12:
\[ 48000 = 2440 \times R \]

9. **Solving for R**:
- Divide both sides by 2440:
\[ R = \frac{48000}{2440} \approx 19.67 \]

10. **Final Result**:
- The rate of interest is approximately 19.67%, which can be rounded to 20%.

### Conclusion:
The rate of interest charged in the installment scheme is **20%**.

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