Question : A and B jointly made a profit of Rs. 1,650 and they decided to share it such that $\frac{1}{3}$ of A's profit is equal to $\frac{2}{5}$ of B's profit. Then the profit of B is:
Option 1: Rs. 700
Option 2: Rs. 750
Option 3: Rs. 850
Option 4: Rs. 800
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Correct Answer: Rs. 750
Solution : Let A's profit as $a$ and B's profit as $b$. Given that $\frac{1}{3}$ of A's profit is equal to $\frac{2}{5}$ of B's profit. $\frac{1}{3}a = \frac{2}{5}b$ $a = \frac{6}{5}b$ The total profit of Rs. 1650 is divided among A and B. $a + b = 1650$ ⇒ $b +\frac{6}{5}b= 1650$ ⇒ $5b+6b=8250$ ⇒ $11b=8250$ ⇒ $b=750$ Hence, the correct answer is Rs. 750.
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