Cost Price Calculation for A
This problem involves calculating the initial cost price given a series of profit and loss transactions.
Step 1: Calculate B's Cost Price
B sold the item to C at a 12% loss. C paid ₹231. This means ₹231 represents 100% - 12% = 88% of the price B paid.
Let the cost price for B be $CP_B$. We can write the equation:
$0.88 \times CP_B = ₹231$
Solving for $CP_B$:
$CP_B = \frac{231}{0.88}$
$CP_B = \frac{23100}{88} = ₹262.50$
Step 2: Calculate A's Cost Price
A sold the item to B at a 25% gain. This means B paid ₹262.50, which is 100% + 25% = 125% of A's original cost price.
Let the cost price for A be $CP_A$. We can write the equation:
$1.25 \times CP_A = CP_B$
$1.25 \times CP_A = ₹262.50$
Solving for $CP_A$:
$CP_A = \frac{262.50}{1.25}$
$CP_A = \frac{26250}{125} = ₹210$
Conclusion
The cost price of the item for A was ₹210.
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