A space research company wants to sell its two products A and B. If the product A is sold at 20% loss and the product B at 30% gain, the company will not lose anything. If the product A is sold at 15% loss and the product B at 15% gain, the company will lose ₹ 6 million in the deal. What is the cost of product B?

### Concept & Balancing Profit and Loss "Not losing anything" is equivalent to saying the total net profit is exactly zero. This means the monetary loss on one item exactly cancels out the monetary gain on the other. ### Step-by-Step Solution * Let the cost of product A be $A$ and product B be $B$. * From the first scenario (no loss): Loss on A = Gain on B $0.20A = 0.30B$ $2A = 3B \Rightarrow A = 1.5B$ * From the second scenario (loss of ₹ 6 million): Loss on A - Gain on B = Net Loss $0.15A - 0.15B = 6$ * Substitute $A = 1.5B$ into the second equation: $0.15(1.5B) - 0.15B = 6$ $0.225B - 0.15B = 6$ $0.075B = 6$ * Solve for B: $B = \frac{6}{0.075} = \frac{6000}{75} = 80$. * The cost of product B is ₹ 80 million. ### Exam Strategy & Shortcut Use the relationship from the first sentence immediately. If 20% A = 30% B, then A = 1.5 B. In the second case, 15% loss on A and 15% gain on B means $15\%(A - B) = 6$. Substitute A with 1.5B: $15\%(0.5B) = 6 \Rightarrow 7.5\%B = 6 \Rightarrow B = 80$. ### Common Pitfall Mixing up the signs in the net loss equation. If the company *loses* 6 million, then (Loss on A) - (Gain on B) = +6. Writing it as (Gain on B) - (Loss on A) = 6 will yield a negative, incorrect answer. ### Final Answer Therefore, the correct answer is **₹ 80 million**.