MAT Exam 2024 Paper

Concept:Profit in a partnership is divided in the ratio of effective capitals, where effective capital = capital invested × time period.Explanation:A starts with $\text{₹}700$ and B starts with $\text{₹}600$.For the first 3 months, A's capital is $\text{₹}700$.So, A's contribution for this period is $700 \times 3 = 2100$.After 3 months, A withdraws $\frac{2}{7}$ of his stock.Withdrawn amount $= \frac{2}{7} \times 700 = \text{₹}200$.Remaining capital $= 700 - 200 = \text{₹}500$.This capital stays for the next 3 months.So, contribution for this period is $500 \times 3 = 1500$.After 6 months, A puts back $\frac{3}{5}$ of what he had withdrawn.Amount put back $= \frac{3}{5} \times 200 = \text{₹}120$.New capital for the last 6 months $= 500 + 120 = \text{₹}620$.Contribution for this period is $620 \times 6 = 3720$.A's total effective capital $= 2100 + 1500 + 3720 = 7320$.B invests $\text{₹}600$ for the full year.B's total effective capital $= 600 \times 12 = 7200$.A's share of profit $= \frac{7320}{7320 + 7200} \times \text{₹}726$.$= \frac{7320}{14520} \times 726 = \frac{61}{121} \times 726 = \text{₹}366$.Answer:A should receive $\text{₹}366$.So, the correct option is B.