Question

Instead of dividing $Rs.180$ among $A,B,C$ in the ratio $\left(1/3\right):\left(1/4\right):\left(1/6\right)$ respectively, it was divided in the ratio $Rs.3:4:6$ mistake. Who gained in the transaction

• A. only $A$
• B. only $B$
• C. only $C$
• D. Both $A$ and $B$

Answer 1

The correct option is C only $C$

Lets do the first division as follows : a : b : c = 1/3 : 1/4 : 1/6

Sum of the ratios = 1/3 + 1/4 + 1/6 = 3/4

A's share = $\frac{1}{3}\times \frac{4}{3}\times 180=80$

B's share = $\frac{1}{4}\times \frac{4}{3}\times 180=60$

C's share = $\frac{1}{6}\times \frac{4}{3}\times 180=40$

if it were divided in the ratio 3 : 4 : 6 we would have :

Sum of ratios = 3 + 4 + 6 = 13

A's share = $\frac{3}{13}\times 180=41\frac{7}{3}$

B's share = $\frac{4}{13}\times 180=55\frac{5}{13}$

C's share = $\frac{6}{13}\times 180=83\frac{1}{13}$

C gained more than he was supposed to get . the rest got less than they were supposed to receive.