Platform-Ticket Revenue Before the Review Meeting
Platform tickets at a small station cost ₹10 each; children below five years and railway pass holders do not need one. In the first week of the month the counter sold 420 tickets on Monday, 380 on Tuesday, 510 on Wednesday, 460 on Thursday, 620 on Friday, 780 on Saturday and 690 on Sunday. The station's weekly target is ₹40,000 from platform tickets. The previous week's total was 3,400 tickets. A ticket vendor tells the station master that 'sales rose 15 per cent this week' and suggests doubling the price to ₹20, arguing that revenue will then easily cross the target. The station master asks you, as the MTS handling the counter, to check the vendor's claims before the review meeting on Monday.
1. Calculate the week's total ticket sales, the daily average and the revenue. Is the target met, and by how much is it missed?
Read the worked answer
Total tickets = 420 + 380 + 510 + 460 + 620 + 780 + 690. Grouping: 420 + 380 = 800; 510 + 460 = 970; 620 + 780 + 690 = 2,090. Total = 800 + 970 + 2,090 = 3,860 tickets.
Daily average = 3,860 ÷ 7 = 551.43, i.e. about 551 tickets per day.
Revenue = 3,860 × ₹10 = ₹38,600.
Target = ₹40,000. Shortfall = 40,000 − 38,600 = ₹1,400, which is 3.5 per cent of the target, or 140 tickets at ₹10. So the week is close but below target, and the gap is small enough that one strong Saturday would have closed it.
2. Check the vendor's claim that sales rose 15 per cent. What is the correct figure, and how large is the overstatement?
Read the worked answer
Increase in tickets = 3,860 − 3,400 = 460. Percentage increase = (460 ÷ 3,400) × 100 = 13.53 per cent, i.e. about 13.5 per cent, not 15 per cent.
The overstatement is 15 − 13.5 = 1.5 percentage points, which is roughly 50 tickets' worth of growth claimed but not achieved. A quick sanity check: 15 per cent of 3,400 is 510, but the actual rise is 460, so the claimed figure is too high.
The sales did rise - just not by the stated amount. In a review meeting the correct response is to accept the direction of the claim and correct the number, because an inflated figure becomes the baseline for next week's target and the error compounds.
3. Evaluate the proposal to double the price to ₹20. How many tickets would then be needed to reach ₹40,000, and what does that imply about the risk?
Read the worked answer
At ₹20, the number of tickets needed for ₹40,000 = 40,000 ÷ 20 = 2,000 tickets.
Current sales are 3,860. So the station would meet the target even if ticket sales fell to 2,000 - a fall of 1,860 tickets, or 48 per cent. On paper the price rise looks very safe.
The risk is not arithmetic but behaviour. A platform ticket is a charge for entering the platform, often bought to see someone off or meet someone; doubling it invites avoidance - people buying one ticket for two people, or entering without a ticket. The revenue target may be met while the number of people on the platform is unrecorded and unmanaged, which is a safety and crowd-control problem, not just a revenue one.
Better advice to the station master: treat the vendor's 15 per cent figure as wrong (13.5 per cent), note the ₹1,400 shortfall, and if the price is raised at all, do it as a trial for one week with a daily count of tickets and a check on unauthorised entry - not as a permanent doubling based on a calculation that assumes demand does not move.