The ladder / Level 4 · New products and services Business math
New-product business math: mixed quiz
Twelve questions across royalties, unit economics, pricing, NPV, break-even with development cost, R&D budgets and market sizing.
By Manoj Sahukar · October 2026 · 6 min read
12 questions drawn from all the new-product business-math topics, from basic to advanced. Each answer links back to its topic page if you want to revise.
How numbers are rounded on these pages. Calculations are done at full precision and rounded only at the end, half up. Rupee amounts are rounded to the nearest rupee unless shown with paise, in which case to the nearest paisa. Percentages are shown to two decimal places, months to one decimal place, years and ratios (such as LTV : CAC) to two, and discount factors to four. Discounting assumes cash flows at the end of each year, compounded yearly. IRR has no exact formula: it is found by repeated trial and shown to two decimal places as a check value. Break-even quantities are rounded up to the next whole unit. All examples and quiz questions are Hypothetical : they show the method, not real prices or rates.
Mixed quiz Pick an answer to see at once whether it is right, with a short explanation. Each question takes one try; your score appears at the end. No answers are sent anywhere. (Without JavaScript, open “Show answer” under each question.)
Royalties and licence fees · Intermediate You can pay a lump sum of ₹10,00,000 or a 5% royalty on a net price of ₹1,000. At what volume do they cost the same?a 2,00,000 units b 20,000 units c 10,000 units d 1,000 units
Show answer Answer: (b) 20,000 units
5% × ₹1,000 = ₹50 a unit. ₹10,00,000 ÷ ₹50 = 20,000 units.
Why the other options are wrong:
(a) That divides by 5, not by 5% of the price.(c) That divides by ₹100, which is 10% of the price.(d) That divides by the whole price.Revise this topic →
Royalties and licence fees · Advanced Royalty is 4% of net sales with a minimum guarantee of ₹5,00,000 a year. Net sales this year were ₹1,00,00,000. Royalty payable?a ₹4,00,000 b ₹5,00,000 c ₹9,00,000 d ₹1,00,000
Show answer Answer: (b) ₹5,00,000
4% of ₹1 crore is ₹4,00,000, below the ₹5,00,000 floor, so you pay ₹5,00,000.
Why the other options are wrong:
(a) That ignores the minimum guarantee.(c) That adds the guarantee to the royalty.(d) That is the shortfall only.Revise this topic →
Unit economics · Intermediate CAC is ₹900. A customer pays ₹300 a month, of which ₹150 is contribution. CAC payback?a 3.0 months b 6.0 months c 0.2 months d 60.0 months
Show answer Answer: (b) 6.0 months
₹900 ÷ ₹150 = 6.0 months.
Why the other options are wrong:
(a) That uses revenue; payback uses contribution.(c) That divides the wrong way round.(d) A slip of ten.Revise this topic →
Unit economics · Advanced Paid ads won 500 customers for ₹4,00,000; a referral scheme won 200 for ₹1,00,000 of referral credits. Blended CAC?a ₹650.00 b ₹800.00 c ₹714.29 d ₹500.00
Show answer Answer: (c) ₹714.29
₹5,00,000 ÷ 700 = ₹714.29.
Why the other options are wrong:
(a) That averages the two channel CACs without weighting by customers.(b) That is paid ads only.(d) That is referrals only.Revise this topic →
Pricing · Intermediate Unit cost ₹1,800. You want a 25% margin on price. Price?a ₹2,250 b ₹2,400 c ₹1,350 d ₹2,025
Show answer Answer: (b) ₹2,400
₹1,800 ÷ (1 − 0.25) = ₹2,400.
Why the other options are wrong:
(a) That is a 25% markup on cost; the margin would be 20%.(c) That takes 25% off cost.(d) Not ₹1,800 ÷ 0.75.Revise this topic →
Pricing · Advanced At ₹600 you expect to sell 10,000 units; at ₹750, 7,000 units. Variable cost ₹400. Which price gives more total contribution?a ₹600, because it sells 3,000 more units b ₹750, by ₹4,50,000 c ₹600, by ₹7,50,000 d They give the same
Show answer Answer: (b) ₹750, by ₹4,50,000
₹600: 10,000 × ₹200 = ₹20,00,000. ₹750: 7,000 × ₹350 = ₹24,50,000.
Why the other options are wrong:
(a) More units at a thinner contribution can earn less.(c) That compares revenue, not contribution.(d) ₹20,00,000 against ₹24,50,000.Revise this topic →
Payback, NPV and IRR · Intermediate ₹1,10,000 will arrive in one year. Your required return is 10%. Present value today?a ₹99,000 b ₹1,00,000 c ₹1,21,000 d ₹1,10,000
Show answer Answer: (b) ₹1,00,000
₹1,10,000 ÷ 1.10 = ₹1,00,000.
Why the other options are wrong:
(a) That takes 10% off; discounting divides by 1.10.(c) That grows the amount instead of discounting it.(d) That ignores the time value of money.Revise this topic →
Payback, NPV and IRR · Intermediate Invest ₹5,00,000 today; receive ₹3,00,000 at the end of year 1 and again at the end of year 2. Required return 10%. NPV?a ₹1,00,000.00 b ₹22,727.27 c ₹20,661.16 d ₹5,20,661.16
Show answer Answer: (c) ₹20,661.16
₹3,00,000 ÷ 1.1 + ₹3,00,000 ÷ 1.21 = ₹2,72,727.27 + ₹2,47,933.88 = ₹5,20,661.16; minus ₹5,00,000 = ₹20,661.16.
Why the other options are wrong:
(a) That ignores discounting.(b) That discounts year 2 with simple interest (÷ 1.20).(d) That is the present value of the inflows; NPV subtracts the investment.Revise this topic →
Break-even with development cost · Intermediate Development cost ₹10,00,000; fixed costs ₹4,00,000 a year; contribution ₹350 a unit. Units needed in year 1 to recover both?a 2,858 units b 1,143 units c 4,000 units d 40,000 units
Show answer Answer: (c) 4,000 units
(₹10,00,000 + ₹4,00,000) ÷ ₹350 = 4,000 units.
Why the other options are wrong:
(a) That recovers only the development cost.(b) That covers only the fixed costs.(d) A slip of ten.Revise this topic →
Break-even with development cost · Advanced Contribution ₹600 a unit, development cost ₹9,00,000. A redesign adds ₹2,00,000 of development cost but cuts variable cost by ₹100. New units to recover development cost?a 1,500 units b 1,834 units c 1,286 units d 1,572 units
Show answer Answer: (d) 1,572 units
₹11,00,000 ÷ ₹700 = 1,571.43, so 1,572 units (round up), against 1,500 before.
Why the other options are wrong:
(a) That is the old figure.(b) That adds the cost but forgets the higher contribution.(c) That uses the higher contribution but forgets the extra cost.Revise this topic →
R&D budgeting · Intermediate Testing was budgeted at ₹8,00,000 and actually cost ₹9,20,000. Variance?a 13.04% over b 15.00% over c 115.00% over d 15.00% under
Show answer Answer: (b) 15.00% over
(₹9,20,000 − ₹8,00,000) ÷ ₹8,00,000 × 100 = 15.00% over.
Why the other options are wrong:
(a) That divides by actual, not budget.(c) That is actual as a percentage of budget.(d) Actual is above budget, so it is over.Revise this topic →
Market sizing · Intermediate SAM is ₹20,00,00,000 and you expect to win 3% of it. SOM?a ₹6,00,00,000 b ₹6,00,000 c ₹60,00,000 d ₹19,40,00,000
Show answer Answer: (c) ₹60,00,000
3% × ₹20,00,00,000 = ₹60,00,000 a year.
Why the other options are wrong:
(a) That uses 30%.(b) That uses 0.03%.(d) That is SAM minus 3%.Revise this topic →