A train starts from station A with some passengers. At station B 10\% of the passengers get down and 100 passengers get in. At station C 50\% get down and 25 get in. At station D 50\% get down and 50 get in making the total number of passengers 200. The number of passengers who boarded the train at station A was
(a)400
(b)500
(c)600
(d)700
Answer
Answer (as printed): B
Explanation
Let the number of passengers who boarded the train at station $A$ be $x$. Then, Number of passengers after the train left station $B$ $$=(100-10) \% \text { of } x+100=90 \% \text { of } x+100=\left(\frac{9 x}{10}+100\right) .$$ Number of passengers after the train left station $C$ $$\begin{aligned} & =(100-50) \% \text { of }\left(\frac{9 x}{10}+100\right)+25=\frac{50}{100}\left(\frac{9 x}{10}+100\right)+25 \\ & =\left(\frac{9 x}{20}+75\right) \end{aligned}$$ Number of passengers after the train left station $D$ $$\begin{aligned} & =(100-50) \% \text { of }\left(\frac{9 x}{20}+75\right)+50 \\ & =\frac{50}{100}\left(\frac{9 x}{20}+75\right)+50=\left(\frac{9 x}{40}+\frac{175}{2}\right) . \\ & \therefore \frac{9 x}{40}+\frac{175}{2}=200 \Rightarrow \frac{9 x}{40}=200-\frac{175}{2}=\frac{225}{2} \\ & \Rightarrow x=\left(\frac{225}{2} \times \frac{40}{9}\right)=500 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.