Kailash wants to sell his television. There are two offers, one at RS 10000 cash and the other at a credit of RS 6440 to be paid after 8 months, money beiing at 18% per annum. Which one is better offer?

Options

A. X 6440 at credit
B. X 6460 in cash
C. X 6440 at credit and X 1000 in cash both
D. X 10000 in cash

Answer

To determine which offer is better for Kailash, we need to calculate the present worth of the second offer, which is Rs 6440 to be paid after 8 months at an interest rate of 18% per annum. We will then compare this present worth with the cash offer of Rs 10,000.

### Step-by-Step Solution:

1. **Identify the Offers:**
- Cash Offer: Rs 10,000
- Credit Offer: Rs 6,440 to be paid after 8 months

2. **Convert the Time Period:**
- The time period for the credit offer is 8 months. To convert this into years, we use:
\[ \text{Time in years} = \frac{8}{12} = \frac{2}{3} \text{ years} \]

3. **Calculate the Present Worth of the Credit Offer:**
- We use the formula for Present Worth (PW):
\[ \text{PW} = \frac{\text{Amount}}{1 + \left(\text{Rate} \times \text{Time}\right)} \]
- Here, the amount is Rs 6440, the rate is 18% per annum (or 0.18), and the time is \(\frac{2}{3}\) years.
- Plugging in the values:
\[ \text{PW} = \frac{6440}{1 + \left(0.18 \times \frac{2}{3}\right)} \]
- Calculate the interest for the time period:
\[ 0.18 \times \frac{2}{3} = 0.12 \]
- Therefore, the formula becomes:
\[ \text{PW} = \frac{6440}{1 + 0.12} = \frac{6440}{1.12} \]

4. **Perform the Division:**
- Now calculate:
\[ \text{PW} = \frac{6440}{1.12} \approx 5750 \]

5. **Compare the Two Offers:**
- Cash Offer: Rs 10,000
- Present Worth of Credit Offer: Rs 5750
- Since Rs 10,000 > Rs 5750, the cash offer is better.

### Conclusion:
Kailash should accept the cash offer of Rs 10,000 as it is greater than the present worth of the credit offer.

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