Mix of profit rates — A trader buys a watch and a wall clock for ₹ 390 in total. He gains 10% on the watch and 15% on the wall clock, and the combined profit is ₹ 51.50. What is the difference between their original prices (wall clock minus watch)?

Introduction / Context:
This is a standard two-variable profit problem. Total cost and total profit are known, and different percentage gains apply to each item. We set up two linear equations in the two unknown costs and solve for the required difference.

Given Data / Assumptions:

• Let watch cost = w; wall clock cost = c.
• w + c = 390.
• Total profit = 0.10w + 0.15c = 51.50.

Concept / Approach:
Solve the linear system by elimination or substitution. The requested quantity is (c − w), the difference in original prices.

Step-by-Step Solution:

Verification / Alternative check:
Profits: watch 10% of 140 = 14; clock 15% of 250 = 37.5; total = 51.5 (matches).

Why Other Options Are Wrong:
₹ 100, ₹ 80, ₹ 90, and ₹ 120 do not satisfy both equations simultaneously.

Common Pitfalls:
Applying the 10% and 15% to the total cost or swapping item roles; always apply percentages to their own costs.

Final Answer:
₹ 110