The Fest Surplus Squeeze
The fest treasurer tables these audited figures for the four flagship events, in rupees: Debate revenue 42,000, cost 30,000; Drama revenue 96,000, cost 1,10,000; Music revenue 1,20,000, cost 84,000; Quiz revenue 28,000, cost 22,000. The council must show a net surplus of at least ₹55,000 to fund a transport subsidy for outstation participants, up from the current ₹40,000. Three proposals are on the table: (i) cancel Drama; (ii) renegotiate Drama's cost down by 20%; (iii) raise the Music ticket price enough to add ₹30,000 in revenue. Council rules cap any single ticket-price increase at 15% of that event's current revenue, and Drama's contract carries a cancellation clause of ₹6,000 payable only if the event is cancelled. The council votes next week.
1. Compute the current net surplus, then the surplus under proposal (i), including the cancellation clause. Does it reach the target?
Read the worked answer
Net per event = revenue − cost:
- Debate: 42,000 − 30,000 = +12,000
- Drama: 96,000 − 1,10,000 = −14,000
- Music: 1,20,000 − 84,000 = +36,000
- Quiz: 28,000 − 22,000 = +6,000
Current total = 12,000 − 14,000 + 36,000 + 6,000 = ₹40,000, which matches the figure in the brief and confirms the four lines are internally consistent.
Proposal (i): cancelling Drama removes a −14,000 line, so the surplus rises to 40,000 + 14,000 = ₹54,000, then the ₹6,000 cancellation clause is paid: ₹48,000.
That misses the ₹55,000 target by ₹7,000. Note the trap: people who read "Drama loses ₹14,000" and stop at 54,000 not only ignore the clause but still land ₹1,000 short. Cancelling the loss-making event is not the same as maximising the surplus.
2. The treasurer writes: "Cancelling Drama is our strongest single lever." Test that claim numerically against proposals (ii) and (iii), applying the council's rules.
Read the worked answer
Proposal (ii), Drama cost down 20%: saving = 0.20 × 1,10,000 = ₹22,000. New surplus = 40,000 + 22,000 = ₹62,000. Meets target.
Proposal (iii), ₹30,000 extra Music revenue: the 15% cap is measured against Music's current revenue of ₹1,20,000, i.e. a maximum of ₹18,000. A ₹30,000 rise is 25% and is not permitted. At the legal maximum the surplus is 40,000 + 18,000 = ₹58,000, which meets the target, but the proposal as written cannot be voted on.
Ranking of single levers: (ii) ₹62,000 > (iii) as permitted ₹58,000 > (i) ₹48,000.
The treasurer's claim is false on two counts. Cancelling Drama is the weakest of the three, because cancellation forfeits ₹96,000 of revenue to save ₹1,10,000 of cost and then pays ₹6,000 for the privilege. The strongest single lever is renegotiation, which keeps the revenue and attacks only the cost.
3. Find the minimum uniform percentage cut in Drama's cost that reaches exactly ₹55,000, and give one non-numeric reason the council might still hesitate.
Read the worked answer
We need to add 55,000 − 40,000 = ₹15,000 to the surplus.
A cost cut of c rupees on Drama raises the surplus by exactly c, so c = ₹15,000.
As a percentage of Drama's cost: 15,000 / 1,10,000 = 0.13636… → 13.64%, i.e. about 13.7%.
Sense check: 13.7% is below the 20% already assumed negotiable, so the target is reachable well inside proposal (ii), and the council has roughly ₹7,000 of headroom (62,000 − 55,000) to absorb slippage.
Non-numeric reason to hesitate: Drama's ₹1,10,000 cost is probably dominated by fixed items - sets, costumes, rights, venue - so a 13.7% cut may mean cutting rehearsal time or production quality, which affects the fest's reputation and next year's sponsorship, not just this year's ledger. The numbers also assume the other three events hit their figures exactly; any shortfall in Music's ₹36,000 contribution has to be covered from the same ₹7,000 buffer.