A dealer buys dry fruit at the rate of Rs. 100,Rs. 80 and Rs. 60 per kg. He bought them in the ratio `12 : 15 : 20` by weight. He in total gets 20% profit by selling the first two and at last he finds he has no gain no loss in selling the whole quantity which he had. What was the percentage loss he suffered for the third quantity ?

Options

A. `40%`
B. `20%`
C. `30%`
D. `50%`

Answer

To solve the problem step by step, we will follow the given information and calculate the required values.

### Step 1: Define the quantities of dry fruits
Let the quantities of the three types of dry fruits be:
- Type A: \( 12x \) kg
- Type B: \( 15x \) kg
- Type C: \( 20x \) kg

### Step 2: Calculate the cost price (CP) of each type
The cost prices per kg are:
- Type A: Rs. 100 per kg
- Type B: Rs. 80 per kg
- Type C: Rs. 60 per kg

Now, we can calculate the total cost price (CP) for each type:
- CP of Type A = \( 100 \times 12x = 1200x \)
- CP of Type B = \( 80 \times 15x = 1200x \)
- CP of Type C = \( 60 \times 20x = 1200x \)

### Step 3: Calculate the total cost price
Now, we can find the total cost price (CP) of all types:
\[ \text{Total CP} = 1200x + 1200x + 1200x = 3600x \]

### Step 4: Calculate the selling price (SP) for Types A and B
The dealer sells Types A and B at a profit of 20%. Therefore, the selling prices will be:
- SP of Type A = \( 120\% \text{ of } 1200x = 1.2 \times 1200x = 1440x \)
- SP of Type B = \( 120\% \text{ of } 1200x = 1.2 \times 1200x = 1440x \)

### Step 5: Calculate the total selling price of Types A and B
Now, we can calculate the total selling price (SP) for Types A and B:
\[ \text{Total SP of A and B} = 1440x + 1440x = 2880x \]

### Step 6: Determine the selling price of Type C
Since the dealer has no gain or loss on the total quantity sold, the total selling price must equal the total cost price:
\[ \text{Total SP} = \text{Total CP} = 3600x \]
Thus, the selling price of Type C can be calculated as:
\[ \text{SP of Type C} = \text{Total SP} - \text{Total SP of A and B} = 3600x - 2880x = 720x \]

### Step 7: Calculate the loss on Type C
The cost price of Type C is \( 1200x \). The selling price is \( 720x \). Therefore, the loss on Type C is:
\[ \text{Loss} = \text{CP of Type C} - \text{SP of Type C} = 1200x - 720x = 480x \]

### Step 8: Calculate the percentage loss on Type C
The percentage loss can be calculated using the formula:
\[ \text{Percentage Loss} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 = \left( \frac{480x}{1200x} \right) \times 100 \]
\[ \text{Percentage Loss} = \left( \frac{480}{1200} \right) \times 100 = 40\% \]

### Final Answer
The percentage loss the dealer suffered for the third quantity (Type C) is **40%**.

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