A dishonest shopkeeper mark up the price of sugar by 20% and gives a discount of 20% and while purchasing from whole-seller he takes 25% more quantity and while selling he gives 10% less quantity. Find his entire profit/loss% in this entire transaction? (in %)

Options

A. A)`33(1)/(3)`
B. B)`16(2)/(3)`
C. C)`8`
D. D)`66(2)/(3)`

Answer

To solve the problem step by step, let's break down the transactions of the dishonest shopkeeper:

### Step 1: Understand the Markup
- The shopkeeper marks up the price of sugar by 20%.
- If the Cost Price (CP) is 100 (for simplicity), the Selling Price (SP) after markup will be:
\[ SP = CP + (20\% \text{ of } CP) = 100 + 20 = 120 \]

**Hint:** Remember that a markup increases the price based on the original cost.

### Step 2: Apply the Discount
- The shopkeeper gives a discount of 20% on the marked price (SP).
- The discount amount is:
\[ \text{Discount} = 20\% \text{ of } 120 = 24 \]
- Therefore, the Selling Price after discount is:
\[ SP = 120 - 24 = 96 \]

**Hint:** Discounts reduce the price from the marked price, so subtract the discount from the SP.

### Step 3: Quantity Purchased from Wholesaler
- The shopkeeper takes 25% more quantity from the wholesaler.
- If he should have bought 1 kg, he actually buys:
\[ \text{Quantity Purchased} = 1 + (25\% \text{ of } 1) = 1 + 0.25 = 1.25 \text{ kg} \]

**Hint:** A percentage increase means you add that percentage of the original amount to the original amount.

### Step 4: Quantity Sold to Customers
- The shopkeeper sells 10% less quantity than he should.
- If he should sell 1 kg, he actually sells:
\[ \text{Quantity Sold} = 1 - (10\% \text{ of } 1) = 1 - 0.1 = 0.9 \text{ kg} \]

**Hint:** A percentage decrease means you subtract that percentage of the original amount from the original amount.

### Step 5: Calculate Effective Cost Price
- The effective cost price for the shopkeeper for 1.25 kg is:
\[ \text{Effective CP} = \frac{100}{1.25} = 80 \text{ (for 1 kg)} \]

**Hint:** When you buy more quantity for the same total cost, the effective cost per unit decreases.

### Step 6: Calculate Profit
- The shopkeeper sells 0.9 kg for 96.
- The effective cost price for 0.9 kg is:
\[ \text{Effective CP for 0.9 kg} = 80 \times 0.9 = 72 \]
- The profit made by the shopkeeper is:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} = 96 - 72 = 24 \]

**Hint:** Profit is calculated as the difference between selling price and cost price.

### Step 7: Calculate Profit Percentage
- The profit percentage is given by:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100 = \left(\frac{24}{72}\right) \times 100 = 33.33\% \]

**Hint:** Profit percentage is always based on the cost price.

### Final Summary
The dishonest shopkeeper makes an overall profit of **33.33%** in this entire transaction.