MAT Exam 2023 Paper

Concept:Profit is distributed in the ratio of effective capital, which is the capital multiplied by the time for which it is invested.Explanation:Let the initial capitals of A, B and C be $5x$, $6x$ and $8x$ respectively.All three invest their initial capitals for the first year.After one year, A increases his capital by 60%, so A's new capital is $5x + 60\% \text{ of } 5x = 8x$.B continues with $6x$.C withdraws 50% of his capital, so C's new capital is $8x - 50\% \text{ of } 8x = 4x$.Now calculate the effective capital contribution over 2 years:A: $5x \times 1 + 8x \times 1 = 13x$B: $6x \times 2 = 12x$C: $8x \times 1 + 4x \times 1 = 12x$Thus, the profit ratio is $13x : 12x : 12x = 13 : 12 : 12$.Answer:The earned profit should be distributed among A, B and C in the ratio $13 : 12 : 12$, i.e. option C.