The Padma Ferry Ghat Ticket Queue
A launch terminal on the Padma sells two classes of tickets: deck (৳120) and cabin (৳450). On a Friday, 620 tickets were sold in total and the counter collected ৳1,41,900. The terminal manager, Rahima, notices that 40% of deck passengers and 25% of cabin passengers bought a ৳30 meal coupon at the same counter, and the coupon revenue (৳6,900) was recorded separately. A junior clerk claims the cabin count must be 180 because '450 times 180 looks about right'. Rahima must verify the class split before submitting the daily report, and she also needs to know whether coupon sales affected the ৳1,41,900 figure.
1. Determine the exact number of deck and cabin tickets sold. Show the algebraic setup and check your answer.
Read the worked answer
Let deck tickets = d and cabin tickets = c.
Equations:
- d + c = 620
- 120d + 450c = 1,41,900
From the first, d = 620 − c. Substituting: 120(620 − c) + 450c = 1,41,900 74,400 − 120c + 450c = 1,41,900 330c = 67,500 c = 204.545...
This is not a whole number, so the stated figures are inconsistent. Rechecking: if c = 205, revenue = 120(415) + 450(205) = 49,800 + 92,250 = 1,42,050, which is ৳150 too high. If c = 204, revenue = 49,920 + 91,800 = 1,41,720, which is ৳180 too low. No integer solution exists.
Conclusion: the total collection or the ticket count is misrecorded. The clerk's guess of 180 cabin tickets is wrong: at c = 180, revenue would be 120(440) + 450(180) = 52,800 + 81,000 = 1,33,800, far below ৳1,41,900. Rahima should flag the discrepancy rather than force a split.
2. Using the coupon data, test whether the recorded ৳6,900 coupon revenue is consistent with any plausible class split, and advise Rahima on what to do.
Read the worked answer
Coupon revenue = 30 × (0.40d + 0.25c) = 6,900, so 0.40d + 0.25c = 230.
Multiply by 20: 8d + 5c = 4,600.
Combine with d + c = 620, i.e. 5d + 5c = 3,100. Subtracting: 3d = 1,500, so d = 500 and c = 120.
Check: 0.40(500) + 0.25(120) = 200 + 30 = 230 coupons; 230 × 30 = ৳6,900. Consistent.
Now test this split against ticket revenue: 120(500) + 450(120) = 60,000 + 54,000 = ৳1,14,000, not ৳1,41,900. So the coupon data and the ticket data contradict each other.
Advice: the coupon ledger supports 500 deck and 120 cabin tickets. The ৳1,41,900 collection figure is overstated by ৳27,900 relative to that split. Rahima should hold the report, recount cash and coupons, and treat the coupon-based split as the working hypothesis because it satisfies two independent constraints.