Logical Reasoning

Arrangements

Hard

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.

Finished product	Raw materials required
Mango smoothie	Mango, Milk
Apple smoothie	Apple, Milk
Banana smoothie	Banana, Milk
Mixed fruit smoothie	Mango, Apple, Banana, Milk
Fruit salad	Mango, Apple, Banana

One unit of milk, mango, apple, and banana cost ₹5, ₹3, ₹2, and ₹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 ₹4 per unit. Leftover raw materials are sold during the last business hour of the day for a loss of ₹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.

Business Hour	Ganga	Kaveri	Narmada
Hour 1	23	19	31
Hour 2	21	22	21
Hour 3	29	30	23
Hour 4 (last hour)	30	27	22

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.

If it is known that three leftover units of mangoes were sold during the last business hour of the day, how many apple smoothies were sold during the day?

Entered answer:

✅ Correct Answer: 6

Slide 1/10

Understanding the set :-

There are 3 women - Ganga, Kaveri, and Narmada

four raw materials (Mango, Apple, Banana and Milk)

and, five finished products (Mango smoothie, Apple smoothie, Banana smoothie, Mixed fruit smoothie and Fruit salad)

To make finished products different raw materials are needed - which are given in the table in set.

Cost of raw materials are -

One unit of milk, mango, apple, and banana cost ₹5, ₹3, ₹2, and ₹1 respectively

Profit = 2* number of raw materials

and, leftovers are sold during the last business hour of the day for a loss of ₹1 per unit.

Set also gives the amount received from sales (revenue) for each woman in four business hours

This is a table question,

In this question we will try to find the products sold by 3 womens in each of the 4 business hours.

Finished Product	Cost Price	Profit	Selling Price
Mango Smoothie	8
Apple Smoothie	7
Banana Smoothie	6
Mixed Fruit	11
Fruit Salad	6

Cost of Finished products :

Mango smoothie -

Raw material required - Mango, Milk - Rs 3 + Rs 5 = Rs 8

Apple smoothie -

Raw material required - Apple, Milk - Rs 2 + Rs 5 = Rs 7

Banana smoothie -

Raw material required - Banana, Milk - Rs 1 + Rs 5 = Rs 6

Mixed fruit -

Raw material required - Mango, Banana, Apple, Milk - Rs 3 + Rs 1 + Rs 2 + Rs 5 = Rs 11

Fruit salad -

Raw material required - Mango, Banana, Apple - Rs 3 + Rs 1 + Rs 2 = Rs 6

Finished Product	Cost Price	Profit	Selling Price
Mango Smoothie	8	4	12
Apple Smoothie	7	4	11
Banana Smoothie	6	4	10
Mixed Fruit	11	8	19
Fruit Salad	6	6	12

We know, Profit = 2* number of raw materials

Therefore, the selling price will become Cost price + profit

Business Hour	Ganga	Kaveri	Narmada
Hour 1	11 + 12	19	19 + 12
Hour 2	11 + 10	12 + 10	11 + 10
Hour 3	19 + 10	19 + 11	11 + 12

Finished Product	Cost Price	Profit	Selling Price
Mango Smoothie	8	4	12
Apple Smoothie	7	4	11
Banana Smoothie	6	4	10
Mixed Fruit	11	8	19
Fruit Salad	6	6	12

Clue 2 says,

Each woman sold either zero or one unit of any single finished product in any hour.

For Ganga :

Hour 1 - Total revenue = 23

We know the selling prices of all the products from the second table.

Therefore only possibility = 12 + 11

Hour 2 - Total revenue = 21

Therefore only possibility = 10 + 11

Hour 3 - Total revenue = 29

Therefore only possibility = 19 + 10

For Kaveri :

Hour 1 - Total revenue = 19

Therefore only possibility = only mixed fruit = 19

Hour 2 - Total revenue = 22

Therefore only possibility = 10 + 12

Hour 3 - Total revenue = 30

Therefore only possibility = 19 + 11

For Narmada :

Hour 1 - Total revenue = 31

Therefore only possibility = 19 + 12

Hour 2 - Total revenue = 21

Therefore only possibility = 10 + 11

Hour 3 - Total revenue = 23

Therefore only possibility = 12 + 11

Business Hour	Ganga	Kaveri	Narmada
Hour 1	11 + 12	19	19 + 12
Hour 2	11 + 10	12 + 10	11 + 10
Hour 3	19 + 10	19 + 11	11 + 12

Finished Product	Cost Price	Profit	Selling Price
Mango Smoothie	8	4	12
Apple Smoothie	7	4	11
Banana Smoothie	6	4	10
Mixed Fruit	11	8	19
Fruit Salad	6	6	12

Business Hour	Ganga	Kaveri	Narmada
Hour 1	A.S + F.S / M.S	M.F	M.F + F.S
Hour 2	A.S + B.S	F.S + B.S	A.S + B.S
Hour 3	M.F + B.S	M.F + A.S	A.S + F.S

We know selling price Rs 12 is of two finished products - mango smoothie and Fruit salad.

But Clue 1 says,

No one except possibly Ganga sold any Mango smoothie.

=> So, lets try to fill the third table,

For ganga :

Hour 1 -

Rs 11 + 12 = Apple salad + mango smoothie/ Fruit salad

Hour 2-

Rs 11 + 10 = Apple smoothie + banana smoothie

Hour 3 -

Rs 19 + 10 = Mixed fruit + Banana smoothie

For Kaveri :

Hour 1 -

Rs 19 = Fruit salad

Hour 2-

Rs 12 + 10 = Fruit salad + banana smoothie

Hour 3 -

Rs 19 + 11 = Mixed fruit + Apple smoothie

For Narmada :

Hour 1 -

Rs 19 + 12 = Fruit salad + Banana smoothie

Hour 2-

Rs 11 + 10 = Apple smoothie + banana smoothie

Hour 3 -

Rs 12 + 11 = Fruit salad + Apple smoothie

Business Hour	Ganga	Kaveri	Narmada
Hour 1	A.S + F.S / M.S	M.F	M.F + F.S
Hour 2	A.S + B.S	F.S + B.S	A.S + B.S
Hour 3	M.F + B.S	M.F + A.S	A.S + F.S

Business Hour	Ganga	Kaveri	Narmada
Hour 1	23	19	31
Hour 2	21	22	21
Hour 3	29	30	23
Hour 4 (last hour)	30	27	22

Clue 3 :

Each woman had exactly one unit each of two different raw materials as leftovers.

Each leftover item is sold at Rs 1 less than their cost price.

Hence One unit of milk, mango, and apple will cost ₹4, ₹2, ₹1

The three possible combinations for the last hour in which raw materials can be sold is :

One unit of milk+ One unit of mango = Rs 4+2 = Rs 6.

One unit of milk+ One unit of apple = Rs 4+1 = Rs 5.

One unit of mango+ One unit of apple = Rs 2+1 = Rs 3

Business Hour	Ganga	Kaveri	Narmada
Hour 1	A.S + F.S / M.S	M.F	M.F + F.S
Hour 2	A.S + B.S	F.S + B.S	A.S + B.S
Hour 3	M.F + B.S	M.F + A.S	A.S + F.S
Hour 4	M.S + F.S + Milk + Mango

Business Hour	Ganga	Kaveri	Narmada
Hour 1	23	19	31
Hour 2	21	22	21
Hour 3	29	30	23
Hour 4 (last hour)	30	27	22

In the last one hour :

Total sale of Ganga is Rs 30. This is the total cost earned by considering selling the finished items and raw materials.

Hence the possible cases are :

(24 + 6) or (25 + 5) or ( 27 + 3).

But, it is not possible to earn 25 and 27 by selling finished products.

Hence she earns Rs 24 which is possible by selling one ( M.S + F.S)

and one raw unit of milk and mango each.

Business Hour	Ganga	Kaveri	Narmada
Hour 1	A.S + F.S / M.S	M.F	M.F + F.S
Hour 2	A.S + B.S	F.S + B.S	A.S + B.S
Hour 3	M.F + B.S	M.F + A.S	A.S + F.S
Hour 4	M.S + F.S + Milk + Mango	A.S + B.S + Milk + Mango / B.S + F.S + Apple + Milk

Business Hour	Ganga	Kaveri	Narmada
Hour 1	23	19	31
Hour 2	21	22	21
Hour 3	29	30	23
Hour 4 (last hour)	30	27	22

Total sale of Kaveri is Rs 27.

This is the total cost earned by considering selling the finished items and raw materials :

Hence the possible cases are : (21 + 6) or (22+5) or (24+3)

Since Kaveri cannot sell mango smoothies

Hence, the possible cases are : (21+6) - Selling one apple smoothie and one banana smoothie and one raw unit of Milk and Mango.

And, (22+5) Selling one Banana smoothie and Fruit Salad, one unit of raw milk, and one unit of Raw Apple.

Business Hour	Ganga	Kaveri	Narmada
Hour 1	A.S + F.S / M.S	M.F	M.F + F.S
Hour 2	A.S + B.S	F.S + B.S	A.S + B.S
Hour 3	M.F + B.S	M.F + A.S	A.S + F.S
Hour 4	M.S + F.S + Milk + Mango	A.S + B.S + Milk + Mango / B.S + F.S + Apple + Milk	M.F + Mango + Apple

Business Hour	Ganga	Kaveri	Narmada
Hour 1	23	19	31
Hour 2	21	22	21
Hour 3	29	30	23
Hour 4 (last hour)	30	27	22

Total sale for Narmada is Rs 22.

The possible cases are : (16+6), (17+5), (19+3).

Among these, the only possible case is 19 + 3.

Selling one unit Mixed Fruit, and one raw unit of Mango and Apple.

Business Hour	Ganga	Kaveri	Narmada
Hour 1	A.S + F.S / M.S	M.F	M.F + F.S
Hour 2	A.S + B.S	F.S + B.S	A.S + B.S
Hour 3	M.F + B.S	M.F + A.S	A.S + F.S
Hour 4	M.S + F.S + Milk + Mango	A.S + B.S + Milk + Mango / B.S + F.S + Apple + Milk	M.F + Mango + Apple

It means each of them sold 1 left over Mango. So we have to count Apple smoothie i.e. b

So 2 + 2 + 2 = 6 is the answer

Question 5

What BEST can be concluded about the number of units of fruit salad sold in the first hour?

Question 6

Which of the following is NECESSARILY true?

Question 7

What BEST can be concluded about the total number of units of milk the three women had in the beginning?

If it is known that three leftover units of mangoes were sold during the last business hour of the day, how many apple smoothies were sold during the day?

Solution

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