MAT Exam 2023 Paper

Concept:After removing equal fixed amounts, the remaining portions are in the ratio $14:21:27$. Use a common multiplier to find the original shares.Explanation:Let the common multiplier be $x$.For A: after removing ₹20, remaining share is $14x$.So, $A - 20 = 14x \Rightarrow A = 14x + 20$For B: after removing ₹40, remaining share is $21x$.So, $B - 40 = 21x \Rightarrow B = 21x + 40$For C: after removing ₹30, remaining share is $27x$.So, $C - 30 = 27x \Rightarrow C = 27x + 30$Total of their original shares is ₹3810.Thus, $(14x+20)+(21x+40)+(27x+30)=3810$Simplifying: $62x + 90 = 3810$So, $62x = 3720$, giving $x = 60$Now find C's original share:$C = 27x + 30 = 27 \times 60 + 30 = 1620 + 30$Therefore, C received ₹1650.Answer:C received ₹1650, i.e. option (A).