Smoothie Scheduling DILR CAT 2021 Slot 1

Ganga, Kaveri, and Narmada are three women who buy four raw materials (Mango, Apple, Banana and Milk) and sell five finished products (Mango smoothie, Apple smoothie, Banana smoothie, Mixed fruit smoothie and Fruit salad). Table-1 gives information about the raw materials required to produce the five finished products. One unit of a finished product requires one unit of each of the raw materials mentioned in the second column of the table.

One unit of milk, mango, apple, and banana cost Rs.5, Rs.3, Rs.2, and Rs.1 respectively. Each unit of a finished product is sold for a profit equal to two times the number of raw materials used to make that product. For example, apple smoothie is made with two raw materials (apple and milk) and will be sold for a profit of Rs.4 per unit. Leftover raw materials are sold during the last business hour of the day for a loss of Rs.1 per unit.

The amount, in rupees, received from sales (revenue) for each woman in each of the four business hours of the day is given in Table-2.

The following additional facts are known.
1. No one except possibly Ganga sold any Mango smoothie.
2. Each woman sold either zero or one unit of any single finished product in any hour.
3. Each woman had exactly one unit each of two different raw materials as leftovers.
4. No one had any banana leftover.

Great! You're working with a complex CAT-level DI-LR puzzle involving:

• Raw material mapping to finished products
• Sales revenue matching
• Inventory leftover logic
• Logical deductions from hourly sales constraints

Here’s a concise step-by-step explanation of how the conclusions were reached from the tables and clues provided:

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🔍 Step-by-step Key Deductions

🧾 Step 1: Understand the Finished Products & Pricing

From Table-1 and Step 1, we get:

Product	Raw Materials Used	Cost	Profit (2×#raw)	Selling Price
Mango Smoothie	Mango + Milk	8	4	12
Apple Smoothie	Apple + Milk	7	4	11
Banana Smoothie	Banana + Milk	6	4	10
Mixed Fruit Smoothie	Mango + Apple + Banana + Milk	11	8	19
Fruit Salad	Mango + Apple + Banana	6	6	12

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⏱️ Step 2: Use the Revenue Data (Table-2) and Constraints

Key Constraints:

1. Only Ganga possibly sold Mango smoothie.
2. Max 1 unit of each product per woman per hour.
3. Each woman had exactly 2 units of leftover raw material.
4. No leftover bananas.
5. Leftover raw material sold at Rs.1 loss/unit → sale value = Rs. 4 (net) = Rs.5 - 1 (milk), Rs.2 - 1 (apple), Rs.3 - 1 (mango)

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✅ Hour 4 – Identifying the Leftovers

Let’s verify final hour sales:

Person	Revenue	Leftovers	Sale Value
Ganga	Rs.5	Milk + Apple → Rs.5
Kaveri	Rs.3	Mango + Apple → Rs.3
Narmada	Rs.6	Milk + Mango → Rs.6

✔️ Satisfies constraint (2 units, no banana, revenue matches leftover sale value).

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✅ Hour 1 Deductions

Ganga:
Revenue = Rs.23
Options:

• 1 Mango S + 1 Apple S → 12 + 11 = 23 ✅
• 1 Apple S + 1 Fruit Salad = 11 + 12 = 23 ✅
  → Either combination works.

Kaveri:
Revenue = Rs.19
→ Only one product possible: Mixed Fruit Smoothie = 19 ✅

Narmada:
Revenue = Rs.31
→ Possible: Mixed Fruit (19) + Fruit Salad (12) ✅

⚠️ From clue: "Only Ganga possibly sold Mango smoothie"
→ So Narmada & Kaveri did not sell Mango Smoothie ⇒ discard Ganga’s first option, she sold:
Apple S + Fruit Salad = 11 + 12 = 23

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✅ Hour 2 Deductions

Person	Revenue	Possibility
Ganga	21	Apple S (11) + Banana S (10) ✅
Kaveri	22	Banana S (10) + Fruit Salad (12) ✅
Narmada	21	Apple S (11) + Banana S (10) ✅

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✅ Hour 3 Deductions

Person	Revenue	Possibility
Ganga	Banana S (10) + Mixed Fruit S (19) = 29 ✅
Kaveri	Apple S (11) + Mixed Fruit S (19) = 30 ✅
Narmada	Apple S (11) + Fruit Salad (12) = 23 ✅

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✅ Summary of Product Sales by Person

Person	Mango S	Apple S	Banana S	Mixed Fruit S	Fruit Salad
Ganga	0	3	2	1	1
Kaveri	0	2	1	2	1
Narmada	0	3	2	1	1

But wait — only Ganga possibly sold Mango Smoothie, and total sold = 0 or 1.

Back to Hour 1:
We earlier said Ganga sold Apple S + Fruit Salad = 23
But that violates the “at most 1 Fruit Salad in Hour 1” from image note.

So we revise:

Let Ganga sold: Mango Smoothie + Apple Smoothie = 12 + 11 = 23 ✅
Kaveri → Mixed Fruit S
Narmada → Mixed Fruit S + Fruit Salad = 19 + 12 = 31 ✅

Now Fruit Salad count in Hour 1 = 1 ✅

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✅ Final Answer Summary

Hour	Ganga	Kaveri	Narmada
1	Mango S + Apple S	Mixed Fruit S	Mixed Fruit S + Fruit S
2	Apple S + Banana S	Banana S + Fruit Salad	Apple S + Banana S
3	Banana S + Mixed Fruit S	Apple S + Mixed Fruit S	Apple S + Fruit Salad
4	Milk + Apple (leftovers)	Mango + Apple	Milk + Mango

Let me know if you want:

• Sales and profit analysis
• Inventory calculation per person
• Leftover purchase cost and net profit sheet

Let’s solve each question based on the deductions from the completed table and constraints in your images.

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