Between two stations the first, second and third class fares were fixed in the ratio 8 : 6 : 3, but afterwards the first class fares were reduced by 1/6 and the second class by 1/12. In a year, number of first, second and third class passengers were respectively 9 : 12 : 26 and the money at the booking offices was Rs. 1088. How much was paid by the first class passengers?
Explanation:
Fare ratio before reduction 8 : 6 : 3
After reduction in first class fare by 1/6 (i.e. actual fare is now 5/6 of original fare), we have (8 × 5)/6 ∶ 6 ∶ 3
⇒ 40/6 ∶ 6 ∶ 3
After reduction of second class fare by 1/12 (i.e. actual fare is now 11/12 of original fare), we have 40/6 ∶ (6 × 11)/12 ∶ 3
⇒ 40/6 ∶ 11/2 ∶ 3 = 80/6 ∶ 11 ∶ 6 = 80 ∶ 66 ∶ 36 = 40 ∶ 33 ∶ 18
Amount of fare collected depends upon fare/passenger×no.of passengers. Thus, combined fare collected ratio is
40 × 9 : 12 × 33 : 26 × 18 = 40 × 3 : 12 × 11 : 26 × 6
⇒ 40 : 4 × 11 : 26 × 2 = 40 : 44 : 52
Total first class fare collected then is 4040+44+52×1088 = 40/136 × 1088 = 40 × 8 = Rs. 320 or 10 × 25
Hence, option (d).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.