If a sum of ₹1170 is distributed among A, B and C in the ratio 2 : 3 : 4 by mistake, instead of \(\frac{1 }{2}\) ∶ \(\frac{1 }{3}\) ∶ \(\frac{1 }{4}\), then who will be benefited most and by how much?

C, ₹250

                   A   :    B   :     C       (A+B+C)

Actual:-      \(\frac{1}{2}\)   :    \(\frac{1}{3}\)   :     \(\frac{1}{4}\)

Actual:-       6   :   4     :    3           13              .........(i)

By Mistake  2   :   3     :    4            9               .........(ii)

(*Note: The amount distributed should be same in every condition)

Therefore, (i) × 9 and (ii) × 13

                   A     :    B    :     C        (A+B+C)

Actual:-       54   :  36    :    27          117 

By Mistake  26   :  39     :   52          117
                                                          

Diff.             28  :   03    :   25

Here,

117R = 1170

1R = 10

According to difference of ratio, C is the most benefited, therefore,

C = 25R = 25 × 10 = 250