MAT Exam 2025 Paper

Concept:Profit is shared in proportion to the equivalent capital invested, which is calculated as investment multiplied by the time period for which it remains in the business.Explanation:Initial investment ratio:$$P:Q:R=\frac{7}{6}:\frac{9}{7}:\frac{11}{9}$$Multiply each term by the LCM of $6,7,9$, which is $126$.$$P=147,\quad Q=162,\quad R=154$$P invests $147$ for the first $7$ months.Contribution $=147 \times 7=1029$.After $7$ months, P withdraws $40\%$, so P continues with $60\%$ of investment.Remaining investment $=147 \times \frac{60}{100}=88.2$.This remains invested for the next $5$ months.Contribution $=88.2 \times 5=441$.Total equivalent capital for P $=1029+441=1470$.Q invests $162$ for the first $8$ months.Contribution $=162 \times 8=1296$.After $8$ months, Q withdraws $25\%$, so Q continues with $75\%$ of investment.Remaining investment $=162 \times \frac{75}{100}=121.5$.This remains invested for the next $4$ months.Contribution $=121.5 \times 4=486$.Total equivalent capital for Q $=1296+486=1782$.R invests $154$ for the whole year.Total equivalent capital for R $=154 \times 12=1848$.Total equivalent capital $=1470+1782+1848=5100$.P's share in profit:$$\frac{1470}{5100} \times 318750 = 91,875$$Answer:P's share in the profit is $91,875$.Correct option: D.