Directions : Ramu and Shyamu decide to sell their cars each at Rs. 36,000. While Ramu decided to give a discount of 8% on the first Rs. 8000,5% on next Rs 12000 and 3% on the rest to buyer Shashi. Shyamu decided to give a discount of 7% on the first 12000, 6% on next 8000 and 5% on the rest to buyer Rajesh. These discounts were, however, subject to the buyers making the payment on time failing which the discount gets reduced by 1% for every delay of a week. In each case, the selling price of 36,000 was arrived at by increasing the cost price by 25%.
If each of them got the payments on time, what is the approximate percentage profit of the person getting the higher profit?

Options

A. `19%`
B. `21%`
C. `25%`
D. `17%`

Answer

To solve the problem step by step, we will calculate the selling price, discounts, and profits for both Ramu and Shyamu.

### Step 1: Calculate the Cost Price (CP)
Given that the selling price (SP) is Rs. 36,000 and it is arrived at by increasing the cost price by 25%, we can calculate the cost price using the formula:

\[ SP = CP + 0.25 \times CP = 1.25 \times CP \]

Rearranging the formula to find CP:

\[ CP = \frac{SP}{1.25} = \frac{36,000}{1.25} = 28,800 \]

### Step 2: Calculate Ramu's Discounts
Ramu gives the following discounts:
- 8% on the first Rs. 8,000
- 5% on the next Rs. 12,000
- 3% on the remaining Rs. 16,000 (since total SP is Rs. 36,000)

**Calculating Ramu's Discounts:**
1. **First Rs. 8,000:**
\[ \text{Discount} = 8\% \text{ of } 8,000 = 0.08 \times 8,000 = 640 \]

2. **Next Rs. 12,000:**
\[ \text{Discount} = 5\% \text{ of } 12,000 = 0.05 \times 12,000 = 600 \]

3. **Remaining Rs. 16,000:**
\[ \text{Discount} = 3\% \text{ of } 16,000 = 0.03 \times 16,000 = 480 \]

**Total Discount for Ramu:**
\[ \text{Total Discount} = 640 + 600 + 480 = 1,720 \]

### Step 3: Calculate Ramu's Profit
Now we can calculate Ramu's profit:

\[ \text{Profit} = SP - CP - \text{Total Discount} \]
\[ \text{Profit} = 36,000 - 28,800 - 1,720 = 5,480 \]

### Step 4: Calculate Shyamu's Discounts
Shyamu gives the following discounts:
- 7% on the first Rs. 12,000
- 6% on the next Rs. 8,000
- 5% on the remaining Rs. 16,000

**Calculating Shyamu's Discounts:**
1. **First Rs. 12,000:**
\[ \text{Discount} = 7\% \text{ of } 12,000 = 0.07 \times 12,000 = 840 \]

2. **Next Rs. 8,000:**
\[ \text{Discount} = 6\% \text{ of } 8,000 = 0.06 \times 8,000 = 480 \]

3. **Remaining Rs. 16,000:**
\[ \text{Discount} = 5\% \text{ of } 16,000 = 0.05 \times 16,000 = 800 \]

**Total Discount for Shyamu:**
\[ \text{Total Discount} = 840 + 480 + 800 = 2,120 \]

### Step 5: Calculate Shyamu's Profit
Now we can calculate Shyamu's profit:

\[ \text{Profit} = SP - CP - \text{Total Discount} \]
\[ \text{Profit} = 36,000 - 28,800 - 2,120 = 5,080 \]

### Step 6: Calculate Percentage Profit for Both
1. **Ramu's Percentage Profit:**
\[ \text{Percentage Profit} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
\[ \text{Percentage Profit} = \left( \frac{5,480}{28,800} \right) \times 100 \approx 19.0\% \]

2. **Shyamu's Percentage Profit:**
\[ \text{Percentage Profit} = \left( \frac{5,080}{28,800} \right) \times 100 \approx 17.6\% \]

### Step 7: Conclusion
The person with the higher profit is Ramu, with an approximate profit percentage of 19%.