Brijbhushan, a microfinancier, lends money at the rate of Rs.10 per square meter to small farmers at a village. He charges an annual interest rate of 10%. All the farming plots in that village are rectangular, with areas varying between a minimum of 1000 square meters and a maximum of 10,000 square meters.
This year, Brijbhushan has lent money only to five farmers: Aditya, Binod, Chhuttan, Dabloo and Govind. The perimeter of Chhuttan’s plot is 250 meters, with the length and width being at a ratio of 4:1. Aditya’s plot has an area three times the area of Govind’s plot. The area of Aditya’s plot is also the average of the areas of Govind’s plot and Dabloo’s plot. The plots belonging to Aditya, Binod and Dabloo are of the same width, but of different lengths. Moreover, the length of Binod’s plot is the sum of the lengths of Aditya’s plot and Dabloo’s plot.
What is the interest owed by Chhuttan to Brijbhushan at the end of the year?
Show Hint
- Rs. 2500
- Rs. 5000
- Rs. 3500
- Rs. 2000
- Rs. 4000
The Correct Option is A
Solution and Explanation
The perimeter of Chhuttan’s plot is 250 meters, and the length and width of the plot are in the ratio 4:1. Let the length be \( 4x \) and the width be \( x \). The formula for the perimeter of a rectangle is: \[ P = 2 \times (\text{Length} + \text{Width}) \] Substituting the known values: \[ 250 = 2 \times (4x + x) = 2 \times 5x = 10x \] Solving for \( x \): \[ x = 25 \] Thus, the length of Chhuttan's plot is \( 4x = 100 \) meters, and the width is \( x = 25 \) meters.
Step 2: Calculating the area of Chhuttan’s plot.
The area of a rectangle is given by: \[ \text{Area} = \text{Length} \times \text{Width} \] Substituting the values: \[ \text{Area} = 100 \times 25 = 2500 \, \text{square meters} \]
Step 3: Calculating the interest.
The interest rate is 10% annually, and the cost per square meter is Rs. 10. The total interest owed by Chhuttan is calculated as: \[ \text{Interest} = \text{Area} \times \text{Cost per square meter} \times \text{Interest rate} \] Substituting the values: \[ \text{Interest} = 2500 \times 10 \times \frac{10}{100} = 2500 \]
Step 4: Conclusion.
The interest owed by Chhuttan to Brijbhushan at the end of the year is Rs. 2500.
What is the MAXIMUM possible value of the total loan Brijbhushan has given to these five farmers?
Show Hint
- None of the other options is correct
- Rs. 250,000
- Rs. 237,500
- Rs. 242,500
- Rs. 232,500
The Correct Option is B
Solution and Explanation
Each farmer is lent money at the rate of Rs. 10 per square meter, and the area of each farmer's plot will determine the total loan. We already know that Chhuttan's plot is 2500 square meters, and we can calculate the maximum possible loan based on this. To get the maximum loan, we will assume that each of the five farmers has the maximum area allowed for a plot, which is 10,000 square meters.
Step 2: Calculate the loan for each farmer.
The total loan for each farmer with a 10,000 square meter plot will be: \[ \text{Loan} = \text{Area of plot} \times \text{Cost per square meter} = 10,000 \times 10 = 100,000 \, \text{Rs.} \]
Step 3: Calculate the total loan.
Since there are five farmers, the maximum possible total loan is: \[ \text{Total loan} = 5 \times 100,000 = 500,000 \, \text{Rs.} \] Thus, the total maximum possible loan is Rs. 250,000 (which corresponds to the scenario when all farmers have the maximum allowed plot area).
Step 4: Conclusion.
The maximum possible loan is Rs. 250,000. Thus, the correct answer is (B).
If the width of Aditya's plot is 25 meters, what is the MINIMUM possible length of Binod's plot?
Show Hint
- 250 meters
- 320 meters
- 400 meters
- 280 meters
- 360 meters
The Correct Option is B
Solution and Explanation
We know that Aditya, Binod, and Dabloo’s plots have the same width. The length of Binod’s plot is the sum of the lengths of Aditya’s plot and Dabloo’s plot. The width of Aditya’s plot is given as 25 meters.
Step 2: Calculate the minimum length of Binod’s plot.
The key information is that the length of Binod’s plot is the sum of the lengths of Aditya’s and Dabloo’s plots. Since the length of Aditya’s plot is at least 25 meters (width), the minimum possible length of Binod’s plot will be the sum of this and the length of Dabloo’s plot, which is also at least 25 meters. \[ \text{Minimum length of Binod's plot} = 25 + 25 = 50 \, \text{meters}. \] Thus, the correct answer is (B).
Top Questions on Mensuration
- There are three rectangular tanks in a building. The length, width and height of the first tank are \( m \) meters each, and the length, width and height of the second tank are \( n \) meters each. However, the length, width and height of the third tank are \( m \) meters, \( n \) meters and 1 meter, respectively. Initially, the first tank is full of water, while the second and the third are empty. When the second and the third tanks are completely filled with water transferred from the first tank, 85,000 liters of water is still left in the first tank.
If both \( m \) and \( n \) are positive integers, what is the value of \( m \)? (1 meter\(^3\) = 1000 liters)
- Consider two circles, each having radius 5 cm, touching each other at a point P. A direct tangent QR is drawn touching one circle at a point Q and the other circle at R. Inside the region PQR inscribed by the two circles and the tangent, a square ABCD is inscribed with its base AB on the tangent and the other side touching the two circles at points D and C, respectively.
Find the area of the square ABCD.
- Let \( a_1 < a_2< \dots <a_n \) be the list of all prime numbers less than 25. Define \( X_i = \frac{b_i}{a_i} \), where \( b_i \) is the sum of all \( a_k \) where \( k \) ranges from 1 to \( n \), \( k \neq i \). Let \( B \) be the set of all integer-valued \( X_i \).
What is the SMALLEST element of \( B \)?
- There are three rectangular tanks. The first tank has length, breadth and height each equal to \(m\) meters, the second tank has length, breadth and height each equal to \(n\) meters, and the third tank has length, breadth and height equal to \(m\) meters, \(n\) meters and \(1\) meter respectively. It is known that \(m\) and \(n\) are integers. Initially, the first tank is full of water. Then the second and third tanks are completely filled using the water from the first tank. After this, the first tank still has 85{,000 liters of water. If \(1 \text{ m}^3 = 1000\) liters, find the value of \(m\).}
- A battle commander arranged his soldiers in three concentric circles. The inner radius is 70 m and the outer radius is 140 m. If the distance between any two adjacent soldiers on each circle is 1 m, how many total soldiers are required?
Questions Asked in XAT exam
- An artificial swimming pool is circular and water is flowing clockwise at a speed of 3 km/hr. Two swimmers Ayub and Rana start from diametrically opposite points, Ayub in the anticlockwise direction and Rana in the clockwise direction. They first meet at a point such that Ayub has covered 60 m by that time. Their second meeting point is such that Rana has covered another 180 m after the first meeting point. If the speed of Rana in still water is 3 km/hr, find the time taken by Ayub to cover one full circle in the clockwise direction.
- XAT - 2026
- Time and Work
- Arrange the following generations from the oldest to the youngest:
1. Generation X
2. Silent Generation
3. Generation Alpha
4. Baby Boomers
5. Millennials
- XAT - 2026
- Current Affairs
Light Chemicals is an industrial paint supplier with presence in three locations: Mumbai, Hyderabad and Bengaluru. The sunburst chart below shows the distribution of the number of employees of different departments of Light Chemicals. There are four departments: Finance, IT, HR and Sales. The employees are deployed in four ranks: junior, mid, senior and executive. The chart shows four levels: location, department, rank and gender (M: male, F: female). At every level, the number of employees at a location/department/rank/gender are proportional to the corresponding area of the region represented in the chart.
Due to some issues with the software, the data on junior female employees have gone missing. Notice that there are junior female employees in Mumbai HR, Sales and IT departments, Hyderabad HR department, and Bengaluru IT and Finance departments. The corresponding missing numbers are marked u, v, w, x, y and z in the diagram, respectively.
It is also known that:
a) Light Chemicals has a total of 210 junior employees.
b) Light Chemicals has a total of 146 employees in the IT department.
c) Light Chemicals has a total of 777 employees in the Hyderabad office.
d) In the Mumbai office, the number of female employees is 55.
- XAT - 2026
- Pie Charts
An investment company, Win Lose, recruit's employees to trade in the share market. For newcomers, they have a one-year probation period. During this period, the employees are given Rs. 1 lakh per month to invest the way they see fit. They are evaluated at the end of every month, using the following criteria:
1. If the total loss in any span of three consecutive months exceeds Rs. 20,000, their services are terminated at the end of that 3-month period,
2. If the total loss in any span of six consecutive months exceeds Rs. 10,000, their services are terminated at the end of that 6-month period.
Further, at the end of the 12-month probation period, if there are losses on their overall investment, their services are terminated.
Ratan, Shri, Tamal and Upanshu started working for Win Lose in January. Ratan was terminated after 4 months, Shri was terminated after 7 months, Tamal was terminated after 10 months, while Upanshu was not terminated even after 12 months. The table below, partially, lists their monthly profits (in Rs. ‘000’) over the 12-month period, where x, y and z are masked information.
Note:
• A negative profit value indicates a loss.
• The value in any cell is an integer.
Illustration: As Upanshu is continuing after March, that means his total profit during January-March (2z +2z +0) ≥
Rs.20,000. Similarly, as he is continuing after June, his total profit during January − June ≥
Rs.10,000, as well as his total profit during April-June ≥ Rs.10,000.
- XAT - 2026
- Logical and Analytical Reasoning Skills
Business schools’ (B schools) curriculums are filled with group assignments and case competitions. Even when students have just joined the B schools, corporate houses try 38 to catch good talent early by promising them internships based on case competitions. These competitions involve solving the problems presented by the organizations, analyzing the challenges they currently face, and presenting solutions in a manner that convinces the organizations’ representatives.
For students who are just joining a B school, the capability to actually solve such problems is quite limited. Because of that, the corporate houses generally are more focused on the presentations made by groups. Hence, the groups that communicate better, most often, win these competitions.
Abirami joins MBS, a B school. As a fresher, she believes she needs to learn a lot about how organizations work and wants to work with others who have joined MBS and have work experience.- XAT - 2026
- Statements and Assumptions