The Fest Juice Counter: Blending, Costing and a New Product
The juice counter at a three-day college fest sells two drinks. Citrus Blast is made by mixing orange concentrate with water in the ratio 2 : 3 by volume; Berry Mix uses berry concentrate and water in the ratio 1 : 2. Orange concentrate costs ₹120 per litre and berry concentrate ₹180 per litre, while water costs nothing. Both drinks are served only in 250 mL cups - Citrus Blast at ₹40 a cup and Berry Mix at ₹45 a cup. On the final day the stall begins with exactly 15 litres of orange concentrate and 12 litres of berry concentrate, and the organisers plan to convert the whole stock into finished drinks, with no wastage and nothing left unsold. A second-year student proposes a third product, 'Sunset Blend': a 250 mL cup containing 125 mL Citrus Blast and 125 mL Berry Mix, to be sold at ₹48. Labour, equipment, cups, ice and straws cost the same for every product and add nothing extra.
1. Which of the two existing drinks earns more profit per litre of finished drink, and by how much? Show the per-cup figures as well.
Read the worked answer
Citrus Blast
- Concentrate fraction = 2/(2+3) = 2/5 of the drink.
- Cost per litre of drink = (2/5) × ₹120 = ₹48.
- Revenue per litre = four 250 mL cups × ₹40 = ₹160.
- Profit = 160 − 48 = ₹112 per litre, i.e. ₹28 per cup.
Berry Mix
- Concentrate fraction = 1/(1+2) = 1/3.
- Cost per litre = (1/3) × ₹180 = ₹60.
- Revenue per litre = four cups × ₹45 = ₹180.
- Profit = 180 − 60 = ₹120 per litre, i.e. ₹30 per cup.
Berry Mix is better by ₹8 per litre (₹2 per cup). The trap is to compare headline prices: Berry Mix is dearer per litre to make (₹60 vs ₹48) but is dearer still to buy.
2. If the entire stock of concentrate is used up and all the drink is sold, what are the total cups sold, total revenue and total profit for the day?
Read the worked answer
Citrus Blast: concentrate is 2/5 of the drink, so 15 L of concentrate yields 15 ÷ (2/5) = 37.5 L of drink = 37.5/0.25 = 150 cups.
- Revenue = 150 × ₹40 = ₹6,000; concentrate cost = 15 × ₹120 = ₹1,800; profit = ₹4,200.
Berry Mix: 12 L ÷ (1/3) = 36 L = 144 cups.
- Revenue = 144 × ₹45 = ₹6,480; concentrate cost = 12 × ₹180 = ₹2,160; profit = ₹4,320.
Day totals: cups = 150 + 144 = 294; revenue = 6,000 + 6,480 = ₹12,480; total concentrate cost = ₹1,800 + ₹2,160 = ₹3,960; profit = 12,480 − 3,960 = ₹8,520 (a margin of about 68.3%).
A useful check: 6,000/160 = 37.5 L and 6,480/180 = 36 L, matching the volumes derived from the ratios.
3. Should the stall launch 'Sunset Blend' at ₹48? Compare it with the two existing drinks on cost and profit per litre, and state the one condition under which the launch could still backfire.
Read the worked answer
Concentrate cost of one Sunset Blend cup
- 125 mL Citrus Blast contains 0.125 × 2/5 = 0.05 L orange concentrate → 0.05 × 120 = ₹6.00.
- 125 mL Berry Mix contains 0.125 × 1/3 = 0.0417 L berry concentrate → 0.0417 × 180 = ₹7.50.
- Total cost per cup = ₹13.50, i.e. ₹54 per litre of blend.
Revenue and profit
- ₹48 per 250 mL = ₹192 per litre.
- Profit = 192 − 54 = ₹138 per litre (₹34.50 per cup).
This beats both Citrus Blast (₹112/L) and Berry Mix (₹120/L), even though it is made from exactly the same two inputs - the gain comes purely from the premium price on a mixed cup. Selling the two halves separately would fetch only ₹20 + ₹22.50 = ₹42.50, so the blend adds ₹5.50 of revenue per cup at identical cost.
The risk: cannibalisation and stock balance. Every blend cup consumes orange and berry concentrate in the ratio 6 : 5, so heavy blend sales drain the Berry stock faster per cup than Berry Mix does and can leave unsold orange concentrate at the end of the day - the exact waste the organisers said they wanted to avoid. Launch only if blend demand is genuinely incremental rather than switched away from existing buyers.