The Fest Booklet Print Quote
The students' union must print 30 copies of a 40-page fest booklet, double-sided, so each copy uses 20 sheets and the job totals 600 sheets (1,200 printed sides). It is 11:30 am and the booklets must reach the venue by 3:30 pm, leaving four hours of printing time. Two quotes are on the table. Shop A, on campus, charges ₹1.20 per printed side, applies a 10% discount to any bill above ₹1,000, and can run 200 sheets an hour. Shop B, in the market, charges ₹0.90 per sheet and counts a double-sided sheet as one sheet, adds a flat ₹250 setup fee, and can run 120 sheets an hour; a pickup trip takes 40 minutes each way. The treasurer has already written "B is cheaper, book it" in the file. The union has ₹1,500 sanctioned and cannot overspend.
1. Compute the total bill at each shop, stating clearly which unit you are counting, and say which is cheaper on price alone.
Read the worked answer
Count consistently. The job is 600 sheets = 1,200 printed sides.
Shop A bills per side: 1,200 × ₹1.20 = ₹1,440. This exceeds ₹1,000, so the 10% discount applies: 1,440 × 0.90 = ₹1,296.
Shop B bills per sheet, and a double-sided sheet counts as one: 600 × ₹0.90 = ₹540, plus the flat ₹250 setup = ₹790.
On price alone B is cheaper by ₹1,296 − ₹790 = ₹506.
The trap is unit mismatch: comparing 600 × ₹0.90 with 1,200 × ₹1.20 treats two different billable units as the same thing. The treasurer's note is arithmetically right for this job size, but it ignores time, and my next answer shows the price advantage evaporates as the job shrinks.
2. Ignoring the deadline and the ₹1,500 cap, at what job size does Shop A become the cheaper option? Show how the ₹1,000 discount threshold changes the comparison.
Read the worked answer
Let s = sheets, so sides = 2s.
No discount zone (bill ≤ ₹1,000, i.e. sides ≤ 833, i.e. s ≤ 416): A = 2.40s; B = 0.90s + 250. Setting equal: 1.50s = 250 → s ≈ 167 sheets. So A is cheaper only below about 167 sheets; above that B wins.
Discount zone (s > 417): A = 2.16s; B = 0.90s + 250. Equal at 1.26s = 250 → s ≈ 198, which lies outside the zone where the discount applies, so inside the discount zone B is cheaper throughout. A sanity check at s = 417: A ≈ ₹901, B ≈ ₹625.
The ₹1,000 threshold therefore flips A from ₹2.40 to ₹2.16 per sheet, but never enough to overtake B. At 600 sheets the price gap is real; it is the clock, not the rupee, that decides the job.
3. Recommend a shop given every constraint in the setup and say what you would tell the treasurer.
Read the worked answer
Recommendation: Shop A, at ₹1,296.
Time is the binding constraint. Shop A needs 600 ÷ 200 = 3 hours, finishing by 2:30 pm - inside the 3:30 pm deadline and inside the ₹1,500 sanction. Shop B needs 600 ÷ 120 = 5 hours, so it would finish around 4:30 pm even if the machine started at 11:30 am, and the 40-minute-each-way pickup adds 80 minutes on top. A ₹506 saving that produces 30 booklets after the event has begun is not a saving.
What I would write to the treasurer: the per-sheet versus per-side difference was missed, B is genuinely cheaper, but B's throughput is 60% of A's and the deadline cannot absorb a 5-hour run. I would ask A to waive or reduce the bill since it is close to the ₹1,000 threshold, and I would record that for any future job under about 167 sheets - or any job with two working days of lead time - B is the correct default.