Question

By mistake instead of dividing Rs. $117$ among $A,B$ and $C$ into the ratio $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$ , it was divided in the ratio of $2:3:4$ . Who gains the most and by how much?

• A. $A,Rs.28$
• B. $B,Rs.3$
• C. $C,Rs.20$
• D. $C,Rs.25$

Answer 1

Answer: (D)

$C,Rs.25$

To convert $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$ into normal ratio, multiply each fraction by the LCM$(2,3,4)=12$
$=12\times \frac{1}{2}:12\times \frac{1}{3}:12\times \frac{1}{4}$
= $6:4:3$
Thus, A would have got $\frac{6}{6+4+3}\times 117=54$
B would have got $\frac{4}{6+4+3}\times 117=36$
And C would have got $\frac{3}{6+4+3}\times 117=27$
Instead Rs. $117$ have been divided in the ratio of $2:3:4$
A gets $\frac{2}{2+3+4}\times 117=26$
B gets $\frac{3}{2+3+4}\times 117=39$
C gets $\frac{4}{2+3+4}\times 117=52$
Thus, by changing the ratio,
A gained $26-54$ = -$28$
B gained $39-36$ = $3$
And C gained $52-27=25$
Thus, C's gain of $25$ is the most.