Profit and Loss — Two motorcycles have the same cost price. One is sold at a 15% profit. The other is sold for ₹ 4800 more than the first motorcycle’s selling price. If the net profit on the combined transaction is 20%, what is the cost price of each motorcycle?

Introduction / Context:
Combined-profit problems require forming equations across multiple sales tied by a shared base (same cost). Here, the second selling price is offset from the first by a fixed rupee amount, and the overall transaction has a specified net profit percentage.

Given Data / Assumptions:

• Certain cost price per bike = x (same for both).
• Bike 1 sold at 15% profit ⇒ SP1 = 1.15x.
• Bike 2 sold at ₹ 4800 more than SP1 ⇒ SP2 = 1.15x + 4800.
• Overall profit on two bikes = 20% on total cost 2x ⇒ total SP = 2.40x.

Concept / Approach:
Equate total selling price from both expressions: SP1 + SP2 must equal 2.40x. Solve for x, the cost of each motorcycle, and then select the matching option.

Step-by-Step Solution:

Verification / Alternative check:
SP1 = 1.15 * 48000 = 55200; SP2 = 55200 + 4800 = 60000; Total SP = 115200 = 2.40 * 48000 = 115200 (consistent).

Why Other Options Are Wrong:
52000, 36000, 42500, and 40000 fail the equation 2.30x + 4800 = 2.40x.

Common Pitfalls:
Adding ₹ 4800 to the cost instead of to SP1, or computing overall 20% on each item individually instead of on the combined cost.

Final Answer:
Rs. 48000