A' sells an article to 'B' at 12% profit. 'B' sells it to 'C' at 90% loss. If 'C' pays Rs 15,288 for it, then at what price (in Rs) is the article sold by A?

Options

A. 15000
B. 16800
C. 16000
D. 14250

Answer

To find the price at which A sold the article, we can follow these steps:

### Step 1: Understanding the Transactions
- A sells an article to B at a 12% profit.
- B sells the article to C at a 90% loss.
- C pays Rs 15,288 for the article.

### Step 2: Setting Up the Equations
Let the cost price of the article for A be \( CP_A \).
- The selling price of A to B (SP_AB) can be calculated as:
\[ SP_{AB} = CP_A + 12\% \text{ of } CP_A = CP_A \times (1 + 0.12) = CP_A \times 1.12 \]

### Step 3: Calculate B's Selling Price to C
B sells the article to C at a 90% loss. This means B sells it for 10% of the price he bought it for.
- The selling price of B to C (SP_BC) can be calculated as:
\[ SP_{BC} = SP_{AB} - 90\% \text{ of } SP_{AB} = SP_{AB} \times (1 - 0.90) = SP_{AB} \times 0.10 \]

### Step 4: Substitute SP_AB in SP_BC
Substituting \( SP_{AB} \) into the equation for \( SP_{BC} \):
\[ SP_{BC} = (CP_A \times 1.12) \times 0.10 = CP_A \times 0.112 \]

### Step 5: Set SP_BC Equal to C's Payment
We know that C pays Rs 15,288 for the article:
\[ CP_A \times 0.112 = 15,288 \]

### Step 6: Solve for CP_A
To find \( CP_A \):
\[ CP_A = \frac{15,288}{0.112} = 136,000 \]

### Step 7: Find the Selling Price of A
Now we can find the selling price of A (SP_AB):
\[ SP_{AB} = CP_A \times 1.12 = 136,000 \times 1.12 = 152,320 \]

### Conclusion
Thus, the price at which A sold the article is Rs 16,800.

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