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📌 Section 1 is Logical reasoning specially designed for CAT
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SET 1 — 🔍 CAT Level
Five graduates from an MBA college—Arjun, Bhavesh, Chetan, Dinesh, and Eshan—have taken loans from XYZ Bank Limited to start their startups. The loan amount is calculated at the rate of Rs. 25 per square meter of land. Each graduate owns a rectangular plot of land, with the area of each plot ranging from a minimum of 2000 to a maximum of 12,000 square meters.
The following information is known:
(i) The perimeter of Chetan's plot is 240 meters, and the ratio of its length to width is 3 : 1.
(ii) The area of Arjun's plot is twice the area of Eshan's plot. It is also equal to the average of the areas of Eshan's and Dinesh's plots.
(iii) The plots owned by Arjun, Bhavesh, and Dinesh have the same width but different lengths.
(iv) The length of Bhavesh's plot is equal to the sum of the lengths of Arjun's and Dinesh's plots.
Question 1
If the bank charges an annual interest rate of 8%, what is the minimum interest that the bank earns from the five graduates at the end of the year?
Question 2
What is the maximum possible total loan amount (in Rs.) that the bank has given to these five graduates?
Question 3
If the length of Bharat's plot is 250 meters and the width of Gopal's plot is half of Deepak's plot width, what is the length (in m) of Gopal's plot?
Question 4
If the lengths of Amit's, Deepak's, Gopal's, and Bharat's plots are in an arithmetic progression, by what percentage is the width of Gopal's plot less than or more than that of Amit's plot?
25% more
50% less
75% more
75% less
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✅ Answers & Explanations
Set 1
Let Gopal’s area = x
From condition (ii):
Amit’s area = 2x
Amit’s area = average of Gopal and Deepak
2x = (x + Deepak)/2
4x = x + Deepak
Deepak’s area = 3x
Since Amit, Bharat, and Deepak have the same width:
Amit : Deepak areas = 2x : 3x
So their lengths = 2 : 3
Let Amit’s length = 2k
Deepak’s length = 3k
Bharat’s length = Amit + Deepak
= 2k + 3k = 5k
So Bharat’s area = 5x
Chirag:
Length : Width = 3 : 1
Let length = 3a, width = a
Perimeter = 240
2(3a + a) = 240
8a = 240
a = 30
So Chirag’s dimensions = 90 × 30
Area = 2700 sq.m
So total areas are:
Gopal = x
Amit = 2x
Deepak = 3x
Bharat = 5x
Chirag = 2700
Total area = 11x + 2700
Since every plot area is between 2000 and 12000:
Bharat’s area = 5x ≤ 12000
x ≤ 2400
Gopal’s area = x ≥ 2000
x ≥ 2000
So, 2000 ≤ x ≤ 2400
Minimum interest
Minimum total area when x = 2000
Total area = 11(2000) + 2700
= 22000 + 2700
= 24700 sq.m
Loan = 24700 × 25
= Rs. 6,17,500
Interest = 8% of 6,17,500
= Rs. 49,400
Answer: Rs. 49,400
Maximum possible total loan
Maximum total area when x = 2400
Total area = 11(2400) + 2700
= 26400 + 2700
= 29100 sq.m
Loan = 29100 × 25
= Rs. 7,27,500
Answer: Rs. 7,27,500
Length of Gopal’s plot
Bharat’s length = 250
But Bharat’s length = 5k
So, 5k = 250
k = 50
Amit’s length = 2k = 100
Deepak’s length = 3k = 150
Let common width of Amit, Bharat, Deepak = w
Deepak’s area = 150w = 3x
So, x = 50w
Gopal’s width = half of Deepak’s width = w/2
Gopal’s area = x = 50w
So, Gopal’s length × w/2 = 50w
Gopal’s length = 100 m
Answer: 100 m
Percentage difference in width
Amit, Deepak, Gopal, Bharat lengths are in AP.
Amit length = 2k
Deepak length = 3k
Bharat length = 5k
So Gopal length must be 4k
Amit’s area = 2x
Amit’s length = 2k
Amit’s width = 2x / 2k = x/k
Gopal’s area = x
Gopal’s length = 4k
Gopal’s width = x / 4k
So Gopal’s width compared to Amit’s width:
= (x/4k) ÷ (x/k)
= 1/4
So Gopal’s width is 75% less than Amit’s width.
Answer: 4) 75% less
⚡ 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.
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