Question : A, B and C started a business. A invested $33 \frac{1}{3}$% of the total capital, B invest $33 \frac{1}{3}$% of the remaining capital and C, the remaining. If the total profit, at the end of a year, was INR 20,250, then the profit of C exceeds the profit of B by:
Option 1: INR 5,200
Option 2: INR 4,500
Option 3: INR 6,750
Option 4: INR 2,700
Correct Answer: INR 4,500
Solution :
Let total capital be $9x$.
Taking $33 \frac{1}{3}$% = $\frac{1}{3}$
Capital of A = $9x \times \frac{1}{3} = 3x$
Capital of B = $(9x - 3x) \times \frac{1}{3} = 2x$
Capital of C = $6x - 2x = 4x$
The profit share of A, B, and C at the end of the year = $3x : 2x : 4x$
Total profit = 20250
⇒ $3x + 2x + 4x = 20250$
⇒ $9x = \frac{20250}{9}$
⇒ $x = 2250$
The profit share of C is more than that of B by = $(4x - 2x) \times 2250 = 4500$
Hence, the correct answer is INR 4,500.
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