CAT 2021 Slot 1 — DILR Question 1
Answer the next 4 questions based on the information given
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.
Table - 1
One unit of milk, mango, apple, and banana cost â¹5, â¹3, â¹2, and â¹1 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 â¹4 per unit. Leftover raw materials are sold during the last business hour of the day for a loss of â¹1 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.
Table - 2
The following additional facts are known.
- No one except possibly Ganga sold any Mango smoothie.
- Each woman sold either zero or one unit of any single finished product in any hour.
- Each woman had exactly one unit each of two different raw materials as leftovers.
- No one had any banana leftover.
What BEST can be concluded about the number of units of fruit salad sold in the first hour?
Answer & solution
- A
Either 0 or 2
- B
Exactly 2
- C
Exactly 1
Either 1 or 2
One unit of milk, mango, apple, and banana cost â¹5, â¹3, â¹2, and â¹1 respectively
We can make the following table for Cost price, Profit and Selling price of each of the products.
âââââââ
Now, we can make the following table for types of products sold be each of the three based on selling price
âââââââ
Note: No one except Ganga sells Mango Smoothie.
After the last hour each woman had exactly one unit each of two different raw materials as leftovers but no one had any banana.
Also, leftover raw materials are sold during the last business hour of the day for a loss of â¹1 per unit
∴ Items left could be
(Milk + Mango) ⇒ CP = 8 ⇒ sold at Rs. 6
(Milk + Apple) ⇒ CP = 7 ⇒ sold at Rs. 5
(Apple + Mango) ⇒ CP = 5 ⇒ sold at Rs. 3
Ganga sells items worth Rs. 30 in last hour, out of these
Case 1: Rs. 6 could be earned from left-overs hence Rs. 24 would be earned from finished products. This is possible by selling Mango Smoothie and Fruit Salad.
Case 2: Rs. 5 could be earned from left-overs hence Rs. 25 would be earned from finished products. This is not possible.
Case 3: Rs. 3 could be earned from left-overs hence Rs. 27 would be earned from finished products. This is not possible.
Hence, Ganga sells Mango Smoothie and Fruit Salad in the last hour and the left-over items are one unit of Milk and Mango each .
Kaveri sells items worth Rs. 27 in last hour, out of these
Case 1: Rs. 6 could be earned from left-overs hence Rs. 21 would be earned from finished products. This is possible by selling Apple Smoothie and Banana Smoothie.
Case 2: Rs. 5 could be earned from left-overs hence Rs. 22 would be earned from finished products. This is possible by selling Banana Smoothie and Fruit Salad.
Case 3: Rs. 3 could be earned from left-overs hence Rs. 24 would be earned from finished products. This is not possible.
Hence, we have 2 cases for Kaveri.
Narmada sells items worth Rs. 22 in last hour, out of these
Case 1: Rs. 6 could be earned from left-overs hence Rs. 16 would be earned from finished products. This is not possible.
Case 2: Rs. 5 could be earned from left-overs hence Rs. 17 would be earned from finished products. This is not possible.
Case 3: Rs. 3 could be earned from left-overs hence Rs. 19 would be earned from finished products. This is possible by selling Mixed Fruit Smoothie.
Hence, Narmada sells Mixed Fruit Smoothie in the last hour and if left with one unit of Apple and Mango each.
Hence, we have the following final table
âââââââ
Narmada sells one unit of Fruit Salad while Ganga may or may not sell one unit of Fruit Salad.
∴ Number of Fruit Salads sold in first hour can be either 1 unit or 2 units.
Hence, option (d).