A, B and C started a business. A invested 33\(\frac{1}{3} \)% of the total capital, B invested 33\(\frac{1}{3} \)% of the remainingcapital and C, the remaining. If the total profit at the end of the year was ₹ 4,050, then find the amount by which the profit of C exceeds the profit of B. 

Given:

A invested 33¹/₃% of the total capital

B invested 33¹/₃% of the remaining capital

C invested the remaining

Total profit = ₹4,050

Formula used:

Profit share ratio is proportional to the investment ratio

Calculation:

Let the total capital be ₹100

A's investment = 33¹/₃% of ₹100 = ₹33¹/₃

Remaining capital = ₹100 - ₹33¹/₃ = ₹66²/₃

B's investment = 33¹/₃% of ₹66²/₃ = ₹22²/₉

Remaining capital for C = ₹66²/₃ - ₹22²/₉ = ₹44⁴/₉

Investment ratio of A:B:C = ₹33¹/₃ : ₹22²/₉ : ₹44⁴/₉

Convert to a common base:

A:B:C = 100/3 : 200/9 : 400/9

Converting to a common ratio:

A:B:C = 300:200:400

Total ratio = 300 + 200 + 400 = 900

Profit share of B = (200/900) × 4050 = ₹900

Profit share of C = (400/900) × 4050 = ₹1800

Difference in profit = ₹1800 - ₹900 = ₹900

∴ The correct answer is option (1).