₨ 3,102 was to be divided among A, B and C in the ratio of 3 : 4 : 5, but by mistake this was distributied in the proportion of \(\frac{1}{3}\) : \(\frac{1}{4}\) : \(\frac{1}{5}\) . How much more does A gain by mistake ?

544.5

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

Actual          3    :    4      :    5             12               .........(i)

By mistake  \(\frac{1}{3}\)   :    \(\frac{1}{4}\)   :     \(\frac{1}{5}\)

                  20   :   15     :    12           47              .........(ii)

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

Therefore, (i) × 47 and (ii) × 12

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

Actual:-         141    :    xx    :    xx         12 × 47 =  564

By Mistake     240   :     xx    :    xx         47 × 12 =  564
                                                                                ↓

Difference      99    :    xx     :   xx                             ↓ ×5.5
                      ↓                                                      3102 (given)   

                      ↓ ×5.5

              Rs. 544.5/- (amount that A got in excess)

** "xx" ⇒ means no need to find the values, because there is no use of these values to find the answer.