By mistake, instead of dividing ₹702 among Ram, Ramesh, and Naresh in the ratio $\frac{1}{3}:\frac{1}{4}:\frac{1}{6}$, it was divided in the ratio of 3 : 4 : 6. Who gained the most and by how much?

Naresh ₹168

Total Amount = Rs 702

Let $\frac{1}{3}$ : $\frac{1}{4}$ : $\frac{1}{6}$ = 4 : 3 : 2

Actual amount they received,

Ram  = (702 x $\frac{4}{9}$) = Rs 312

Ramesh  = (702 x $\frac{3}{9}$) = Rs 234

Naresh  = (702 x $\frac{2}{9}$) = Rs 156

But, due to mistake they received money in the ratio 3 : 4 : 6

Ram  = (702 x $\frac{3}{13}$) = Rs 162

Ramesh  = (702 x $\frac{4}{13}$) = Rs 216

Naresh  = (702 x $\frac{6}{13}$) = Rs 324

loss of Ram = Rs 150, loss of Ramesh = Rs 18, gain of Naresh = Rs  168

Thus, Naresh gained Rs 168 in the transaction