Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: 2006 · Marks: · Difficulty:
Railway fares of 1st, 2nd and 3rd classes between two stations were in the ratio of $8: 6: 3$. The fares of 1st and 2nd class were subsequently reduced by $\frac{1}{6}$ and $\frac{1}{12}$ respectively. If during a year the ratio between the passengers of 1st, 2nd and 3rd classes was 9 : 12 : 26 and the total amount collected by the sale of tickets was ₹ 1088, then find the collection from the passengers of 1st class.
(a)₹ 260
(b)₹ 280
(c)₹ 300
(d)₹ 320
Answer
Answer (as printed): D
Explanation
Let the initial fares of 1st, 2nd and 3rd class be ₹ $8 x$, ₹ $6 x$ and ₹ $3 x$ respectively. Revised fare of 1st class $=\frac{5}{6}$ of $₹ 8 x=₹\left(\frac{20 x}{3}\right)$. Revised fare of 2nd class $=\frac{11}{12}$ of $₹ 6 x=₹\left(\frac{11 x}{2}\right)$. Let the number of passengers of 1st, 2nd and 3rd class be $9 y, 12 y$ and $26 y$ respectively. Then, $\frac{20 x}{3} \times 9 y+\frac{11 x}{2} \times 12 y+3 x \times 26 y=1088$ $$\begin{aligned} & \Rightarrow 60 x y+66 x y+78 x y=1088 \Rightarrow 204 x y=1088 \\ & \Rightarrow x y=\frac{1088}{204}=\frac{16}{3} . \end{aligned}$$ ∴ Collection from passengers of 1st class $=60 x y$ $$=₹\left(60 \times \frac{16}{3}\right)=₹ 320 .$$
Explanation as extracted from the printed page; notation may be imperfect.