MAT Exam 2025 Paper

Concept:Use a variable for A's share and form an equation from the total distributed amount.Explanation:Let A's share be $x$.B gets $17.5\%$ more than A, so B's share is $x + \frac{17.5}{100}x = \frac{47}{40}x$.C gets one-third of the sum of A and B.Therefore, C's share is $\frac{1}{3}\left(x+\frac{47}{40}x\right)=\frac{1}{3}\left(\frac{87}{40}x\right)=\frac{87}{120}x$.The total amount distributed is $A+B+C+D=1{,}75{,}000$.Substitute $D=42{,}760$: $x+\frac{47}{40}x+\frac{87}{120}x+42{,}760=1{,}75{,}000$.So $x+\frac{47}{40}x+\frac{87}{120}x=1{,}32{,}240$.Making denominators equal to 120 gives $\frac{120x+141x+87x}{120}=1{,}32{,}240$.Thus, $\frac{348}{120}x=1{,}32{,}240$, which gives $x=\frac{1{,}32{,}240 \times 120}{348}=45{,}600$.So A gets ₹$45{,}600$.B's share is $\frac{47}{40}\times 45{,}600=53{,}580$.C's share is $\frac{1}{3}(45{,}600+53{,}580)=\frac{1}{3}(99{,}180)=33{,}060$.Required difference is $53{,}580-33{,}060=20{,}520$.Answer:₹$20{,}520$, which is Option A.