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📌 Section 1 is Logical reasoning specially designed for CAT
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SET 1 — 🔍 CAT Level
The table below gives the process of manufacturing four different products – A, B, C and D – each of which has to pass through all the four machines 1, 2, 3 and 4.
Manufacturing Details
Machine | A | B | C | D |
|---|---|---|---|---|
1 | (6, 1) | (4, 1) | (3, 1) | (6, 2) |
2 | (8, 2) | (5, 1) | (6, 2) | (4, 1) |
3 | (3, 1) | (4, 2) | (6, 1) | (5, 1) |
4 | (5, 1) | (4, 1) | (5, 1) | (6, 2) |
Each product should pass through machines 1, 2, 3 and 4 in that order, before it is ready.
For each machine, the first figure in the bracket indicates the quantity (in units) of the corresponding product produced, while the second figure indicates the time taken (in hours) to produce that quantity.
For example, Machine 1 can produce 6 units of Product D in 2 hours, or 1 unit every 20 minutes.
Each day, only one type of product can be made and the working time is from 9:30 a.m. to 5:30 p.m. (8 hours). All machines are operated in such a way that any unit that is started on a day is finished by the end of that day (5:30 p.m.).
The selling prices and the profit percentage on each of the products are given below.
Selling Price and Profit
Product | A | B | C | D |
|---|---|---|---|---|
Selling Price | 275 | 504 | 234 | 345 |
Profit Percentage* | 10 | 12 | 30 | 15 |
* Profit percentage is as a percentage of cost price.
All the machines operate simultaneously.
Question 1
What is the maximum number of units of any product that can be manufactured in a day?
a) 20
b) 21
c) 22
d) 23
Question 2
If the maximum possible revenue is to be generated in a day, which product should be manufactured on that day? (All the units manufactured are sold on the same day.)
a) A
b) B
c) C
d) D
Question 3
To get the maximum possible profit on a single day, which of the following should be produced?
a) D
b) C
c) A
d) B
Question 4
By what percentage does the cost of producing one unit of B exceed that of one unit of D?
a) 30%
b) 40%
c) 50%
d) 60%
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✅ Answers & Explanations
Set 1
Working time per day = 8 hours
For each product, each unit must pass through Machine 1 → Machine 2 → Machine 3 → Machine 4.
For a production line:
Total time for n units = Time for first unit through all machines + (n - 1) × time of slowest machine
Because after the first unit moves ahead, the machines can work simultaneously.
Question 1
Product A
Machine-wise time per unit:
M1 = 1/6 hr
M2 = 2/8 = 1/4 hr
M3 = 1/3 hr
M4 = 1/5 hr
Time for first unit:
= 1/6 + 1/4 + 1/3 + 1/5
= 19/20 hr
Slowest machine = 1/3 hr per unit
For n units:
19/20 + (n - 1)(1/3) ≤ 8
Maximum n = 22
Product B
M1 = 1/4
M2 = 1/5
M3 = 2/4 = 1/2
M4 = 1/4
Time for first unit:
= 1/4 + 1/5 + 1/2 + 1/4
= 6/5 hr
Slowest machine = 1/2 hr
6/5 + (n - 1)(1/2) ≤ 8
Maximum n = 14
Product C
M1 = 1/3
M2 = 2/6 = 1/3
M3 = 1/6
M4 = 1/5
Time for first unit:
= 1/3 + 1/3 + 1/6 + 1/5
= 31/30 hr
Slowest machine = 1/3 hr
31/30 + (n - 1)(1/3) ≤ 8
Maximum n = 21
Product D
M1 = 2/6 = 1/3
M2 = 1/4
M3 = 1/5
M4 = 2/6 = 1/3
Time for first unit:
= 1/3 + 1/4 + 1/5 + 1/3
= 67/60 hr
Slowest machine = 1/3 hr
67/60 + (n - 1)(1/3) ≤ 8
Maximum n = 21
Maximum units possible = 22
Answer: a) 20? Actually from calculation, it is 22.
Correct answer: c) 22
Question 2
Revenue = Number of units × Selling price
A: 22 × 275 = 6050
B: 14 × 504 = 7056
C: 21 × 234 = 4914
D: 21 × 345 = 7245
Maximum revenue is from Product D.
Answer: d) D
Question 3
Profit percentage is on cost price.
For A:
SP = 275, Profit = 10%
CP = 275/1.10 = 250
Profit per unit = 25
Total profit = 22 × 25 = 550
For B:
SP = 504, Profit = 12%
CP = 504/1.12 = 450
Profit per unit = 54
Total profit = 14 × 54 = 756
For C:
SP = 234, Profit = 30%
CP = 234/1.30 = 180
Profit per unit = 54
Total profit = 21 × 54 = 1134
For D:
SP = 345, Profit = 15%
CP = 345/1.15 = 300
Profit per unit = 45
Total profit = 21 × 45 = 945
Maximum profit is from Product C.
Answer: b) C
Question 4
Cost price of B = 450
Cost price of D = 300
Percentage by which B exceeds D:
= (450 - 300)/300 × 100
= 150/300 × 100
= 50%
Answer: c) 50%
Final Answers:
c) 22
d) D
b) C
c) 50%
⚡ Brain teasers are not just about getting the right answer — they train you to think differently under pressure.
Stay consistent with your daily practice, challenge your assumptions, and keep sharpening your reasoning skills.
See you in tomorrow’s challenge!