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### 1. The value of \( \sqrt{81} \div \sqrt{0.09} \) is:
We calculate each square root individually.
- \( \sqrt{81} = 9 \)
- \( \sqrt{0.09} = 0.3 \)

Now divide:  
\( 9 \div 0.3 = 30 \).

**Answer: (D) 30**

---

### 2. If it takes 40 days for 120 men to complete a work, how long will it take for 80 men to complete the same work?

This is an inverse proportion problem since fewer men will take more time to complete the work.

The formula is:
\[
\text{Days for 80 men} = \frac{120 \times 40}{80} = 60 \text{ days}
\]

**Answer: (B) 60 days**

---

### 3. The value of \( \sqrt[3]{1.331} \times \sqrt{0.001331} \) is:
- \( \sqrt[3]{1.331} \approx 1.1 \)
- \( \sqrt{0.001331} \approx 0.0365 \)

Multiplying these:
\[
1.1 \times 0.0365 \approx 0.04
\]

**Answer: (B) 0.1331**

---

### 4. The marked price of a pen is ₹10 and the shopkeeper allows a discount of 10% on it. The sale price is:
10% discount means reducing the price by 10% of ₹10.

\[
\text{Discount} = 10\% \times 10 = 1
\]
\[
\text{Sale Price} = 10 - 1 = ₹9
\]

**Answer: (B) ₹9**

---

### 5. The value of \( \sqrt[3]{103^3 + 93^3 - 13^3} \) is:

Let's calculate each part:
- \( 103^3 = 1092727 \)
- \( 93^3 = 804357 \)
- \( 13^3 = 2197 \)

Now sum:
\[
1092727 + 804357 - 2197 = 1896887
\]
The cube root:
\[
\sqrt[3]{1896887} \approx 123
\]

**Answer: (A) 12**

---

### 6. Which of the following is a triangular number as well as a square number?

- \( 49 \) is both a square number ( \( 7^2 \) ) and a triangular number (7th triangular number: \( T_7 = \frac{7 \times 8}{2} = 28 \)).

**Answer: (D) 49**

---

Do you need any further clarifications or explanations for these solutions?  

Here are some related questions you might explore:
1. How do inverse proportions work in general problem-solving?
2. What is the general formula for calculating a triangular number?
3. How can one quickly calculate cube roots of large numbers?
4. How do you identify square numbers and triangular numbers more efficiently?
5. What other types of proportional relationships appear in work-time problems?

**Tip:** For time-work problems, always remember that fewer workers take more time, so the relationship is inversely proportional.

1. The value of √81 ÷ √0.09 is:
2. If it takes 40 days for 120 men to complete a work, how long will it take for 80 men to complete the same work?
3. The value of ∛1.331 × √0.001331 is:
4. The marked price of a pen is ₹10 and the shopkeeper allows a discount of 10% on it. The sale price is:
5. The value of ∛(103³ + 93³ - 13³) is:
6. Which of the following is a triangular number as well as a square number?

Explore a set of math problems involving square and cube roots, inverse proportions, and discount calculations. Detailed solutions provided for each problem, suitable for students in Grades 8-10. Learn about square and triangular numbers and improve your problem-solving skills.

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