1. The expenses of a hostel are partly constant and partly directly proportional to the number of boarders. When the number of boarders is 120, the total expense is ₹2000, and when the number of boarders is 100, the expense is ₹1700. Calculate and write the number of boarders when the expense is ₹1880.

2. Under the condition that no interest will be charged if the money is repaid within two years, three friends borrowed ₹6000, ₹8000, and ₹5000 respectively from a cooperative bank to jointly purchase four cycle rickshaws. After two years, after deducting all expenses, their total income amounted to ₹30,400. They divided this income in proportion to their capital contributions and then repaid their individual bank loans. Now, calculate how much money each person will have left in hand and what the ratio of the remaining amounts will be.

3. Puja, Uttam, and Meher started a partnership business by investing ₹5,000, ₹7,000, and ₹10,000 respectively, under the following conditions: (i) Monthly business operating expenses are ₹125. (ii) Puja and Uttam will each receive ₹200 per month for bookkeeping duties. At the end of the year, if the total profit is ₹6,960, calculate how much profit each person will receive.

4. If \(n\) is an even number, then the median will be the average of the \(\left(\cfrac{n}{2}\right)\)-th and \(\left(\cfrac{n}{2}−1\right)\)-th observations.

5. If \(4\), \(5 + x\), \(2x + 1\), and \(14\) are in continued proportion and \(x\) is a positive number, then what is the value of \(x\)?

(a) 1 (b) 2 (c) 4 (d) 3

6. From each of the numbers 6, 10, 9, and 16, if the same number is subtracted, the resulting values are in proportion. What is that number?

(a) 1 (b) 2 (c) 3 (d) 4

7. If the numbers \((2 + x)\), \((8 + x)\), and \((26 + x)\) are in continued proportion, then what is the value of \(x\)?

(a) 4 (b) 3 (c) 2 (d) 1

8. Prafulla Babu in our village bought a total of 350 chili saplings to plant in his rectangular field. While planting them in rows, he observed that if the number of saplings in each row is 24 more than the number of rows, then 10 saplings remain extra. Find and write the number of rows.

9. "The panchayat committee of Bakultala village has taken up a plan to provide electricity to households that do not have power connections. In this village, there are 1200 households without electricity. If every year, 75% of the households without electricity receive power connections compared to the previous year, then calculate and write the number of unelectrified households remaining in Bakultala village after 2 years."

10. The weight data of 35 students in Nibedita’s class is as follows: ```html

11. Total number of students = 84, and the distribution of students’ marks is as follows: | Marks Obtained | 0–10 | 10–30 | 30–60 | 60–70 | 70–90 | |----------------|------|--------|--------|--------|--------| Median class interval’s class width.

(a) 10 (b) 20 (c) 30 (d) 40

12. Every real number is an irrational number. This statement is **false**. While irrational numbers are a subset of real numbers, real numbers also include **rational numbers**—like integers, fractions, and terminating or repeating decimals. So not every real number is irrational. If you'd like, I can break down the number system hierarchy to make this crystal clear! ????