A miner sells a diamond to a trader at a profit of 40%, and the trader then sells it to a customer at a further profit of 25%. If the customer pays Rs 56 lakhs for the diamond, what was the cost of the diamond to the miner (in lakhs)?

Introduction / Context:
This problem involves successive profits made by different people in a chain of sales. The miner sells to the trader at one profit percentage, and then the trader sells to the final customer at another profit percentage. We are given the final selling price and must deduce the original cost to the miner. It tests understanding of compound percentage profit over multiple stages of resale.

Given Data / Assumptions:

• Miner sells to trader at 40% profit.
• Trader sells to customer at 25% profit on his buying price.
• Customer pays Rs 56 lakhs.
• We denote the miner cost price by C lakhs.
• We need to determine C.

Concept / Approach:
Let C be the cost price for the miner:

• Trader's cost price = C * (1 + 40/100) = 1.4C.
• Customer's price (final selling price) = trader's cost * (1 + 25/100) = 1.4C * 1.25.
• Simplify 1.4 * 1.25 to find the overall multiplication factor from miner's cost to customer's payment.
• Then set that equal to 56 and solve for C.

Step-by-Step Solution:
Let miner cost price be C lakhs. Trader buys from miner at 40% profit, so trader cost price = 1.4C. Trader sells to customer at 25% profit, so final selling price = 1.25 * 1.4C. 1.25 * 1.4 = 1.75. Therefore customer price = 1.75C. Given that customer pays 56 lakhs, so 1.75C = 56. C = 56 / 1.75. C = 32 lakhs. Thus the diamond cost the miner Rs 32 lakhs.

Verification / Alternative check:
Verify by forward calculation:

• Miner cost price = 32 lakhs.
• Trader cost price = 32 * 1.4 = 44.8 lakhs.
• Customer price = 44.8 * 1.25 = 56 lakhs.

These values exactly match the given final selling price. Also, miner profit = 44.8 - 32 = 12.8 lakhs, which is 40% of 32. Trader profit = 56 - 44.8 = 11.2 lakhs, which is 25% of 44.8. Everything is consistent, so C = 32 lakhs is correct.

Why Other Options Are Wrong:
If miner cost were 30 lakhs, trader cost would be 42 lakhs and final selling price 52.5 lakhs, not 56 lakhs. For 28 lakhs, final selling price would be 49 lakhs. For 25 lakhs, final selling price would be 43.75 lakhs. For 24 lakhs, final selling price would be 42 lakhs. None of these values match the customer payment of 56 lakhs.

Common Pitfalls:
Learners sometimes add profit percentages directly (40% + 25% = 65%) and treat the total multiplier as 1.65, which is incorrect because each percentage is applied to a different base. Another mistake is to treat 56 as profit instead of final selling price. Always work stepwise through each transaction and remember that successive percentages multiply, not simply add.

Final Answer:
The cost of the diamond to the miner was 32 lakhs.