UPSC CDS 2 2020 Math Paper

Concept:Profit sharing is based on the product of capital invested and the time it is used.Explanation:The given capital ratio is $\frac{1}{3} : \frac{1}{4} : \frac{1}{5}$.Multiply by the LCM (60) to get integers: $20 : 15 : 12$.Let the investments be $20x$, $15x$, and $12x$ respectively.The first person withdraws half his capital after 4 months.So, for the first 4 months, his capital is $20x$; for the remaining 8 months, it is $10x$.His equivalent investment = $(20x \times 4) + (10x \times 8) = 80x + 80x = 160x$.Second person’s equivalent = $15x \times 12 = 180x$.Third person’s equivalent = $12x \times 12 = 144x$.Total equivalent investment = $160x + 180x + 144x = 484x$.Profit sharing ratio = $160 : 180 : 144$, which simplifies to $40 : 45 : 36$ (dividing by 4).Sum of ratio parts = $40 + 45 + 36 = 121$.First person’s share = $\frac{96800}{121} \times 40 = 800 \times 40 = 32000$.Answer:Rs. 32,000.