The majority against a certain motion is equal to 8\% of the total number of voting. If 14 of those who voted against it had voted for it, the motion would have been carried by 4 votes. Find the number of votes for and against the motion.
(a)112, 126
(b)138, 162
(c)128, 144
(d)148, 172
Answer
Answer (as printed): B
Explanation
Let the number of votes for the motion be F and those against the motion be A. Let the total number of votes be $x$. Then, $(\mathrm{F}+14)-(\mathrm{A}-14)=4 \Rightarrow \mathrm{A}-\mathrm{F}=24$. $$\therefore 8 \% \text { of } x=24 \Rightarrow x=\frac{24 \times 100}{8}=300 .$$ So, $$\begin{aligned} \mathrm{F}+\mathrm{A}=300 & \Rightarrow \mathrm{F}+(\mathrm{F}+24)=300 \\ & \Rightarrow 2 \mathrm{F}=276 \Rightarrow \mathrm{F}=138 \\ \mathrm{A}=(300-138) & =162 \end{aligned}$$