A sold an article to B at a loss of 20%, and B sold it to C at a profit of 32%. C sold it to D at a loss of 20% If A's loss is ₹35 less than that of C, then B boght the article for:

Options

A. ₹2,800
B. ₹2,500
C. ₹2,940
D. ₹2,750

Answer

To solve the problem step by step, let's denote the following:

- Let the cost price of A (CP_A) be ₹100.

### Step 1: Calculate Selling Price of A (SP_A)
A sold the article to B at a loss of 20%.
- Loss = 20% of CP_A = 20% of ₹100 = ₹20
- Therefore, SP_A = CP_A - Loss = ₹100 - ₹20 = ₹80

**Hint:** To find the selling price after a loss, subtract the loss from the cost price.

### Step 2: Calculate Selling Price of B (SP_B)
B sold the article to C at a profit of 32%.
- Profit = 32% of SP_A = 32% of ₹80 = ₹25.60
- Therefore, SP_B = SP_A + Profit = ₹80 + ₹25.60 = ₹105.60

**Hint:** To find the selling price after a profit, add the profit to the cost price.

### Step 3: Calculate Selling Price of C (SP_C)
C sold the article to D at a loss of 20%.
- Loss = 20% of SP_B = 20% of ₹105.60 = ₹21.12
- Therefore, SP_C = SP_B - Loss = ₹105.60 - ₹21.12 = ₹84.48

**Hint:** To find the selling price after a loss, subtract the loss from the selling price.

### Step 4: Calculate Loss of A and C
- A's loss = CP_A - SP_A = ₹100 - ₹80 = ₹20
- C's loss = SP_B - SP_C = ₹105.60 - ₹84.48 = ₹21.12

### Step 5: Set up the equation based on the problem statement
According to the problem, A's loss is ₹35 less than C's loss:
- A's loss = C's loss - ₹35
- Therefore, ₹20 = ₹21.12 - ₹35

This equation does not hold true, so we need to adjust our understanding of the losses.

### Step 6: Correct the equation
From the problem:
- A's loss = C's loss - ₹35
- Therefore, ₹20 = ₹21.12 - ₹35
- Rearranging gives us:
- C's loss = A's loss + ₹35
- ₹21.12 = ₹20 + ₹35
- This means we need to find a relationship between the losses.

### Step 7: Solve for B's cost price
Let B's cost price be CP_B. We know:
- CP_B = SP_A = ₹80 (since B bought it from A for ₹80).

### Conclusion
Thus, B bought the article for **₹80**.

**Final Answer:** B bought the article for ₹80.