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Let's solve the questions one by one from the image you provided:

### **Q.14)**
*Two pipes A and B fill a tank. Pipe B fills the tank twice as fast as Pipe A. If both pipes together can fill the tank in 45 minutes, how much time will Pipe A take to fill the tank alone?*

Let:
- Pipe A's rate = 1/x (portion of the tank filled per minute).
- Pipe B's rate = 2/x (since B is twice as fast as A).

Together, they fill the tank in 45 minutes:
\[
\frac{1}{x} + \frac{2}{x} = \frac{1}{45}
\]
\[
\frac{3}{x} = \frac{1}{45}
\]
\[
x = 45 \times 3 = 135 \text{ minutes.}
\]

Therefore, **Pipe A** alone will take **135 minutes** to fill the tank.

**Answer: 2. 135**

---

### **Q.15)**
*The percentage of disqualified applicants for the driving license test in September.*

Given:
- **Appeared applicants in September = 2500**
- **Qualified applicants = 1200**

Disqualified applicants = \( 2500 - 1200 = 1300 \)

Percentage of disqualified applicants:
\[
\frac{1300}{2500} \times 100 = 52\%
\]

So, the answer is **52%** disqualified applicants.

---

### **Q.16)**
*What percentage of the total expenditure in 2006 is compared to 2009?*

From the table:
- **Total expenditure in 2006**: \( 225 + 98 + 4.25 + 29.7 + 110 = 467.95 \) lakh rupees.
- **Total expenditure in 2009**: \( 295 + 145 + 6.25 + 49.6 + 118 = 613.85 \) lakh rupees.

Percentage of 2006 compared to 2009:
\[
\frac{467.95}{613.85} \times 100 \approx 76.23\%
\]

Since the nearest answer is 76.09%, the closest option is **3.76.09%**.

**Answer: 3. 76.09%**

---

### **Q.17)**
*The expression \( 7^{15} + 7^{16} + 7^{17} \) is divisible by which of the following numbers?*

Factor the expression:
\[
7^{15} (1 + 7 + 7^2) = 7^{15} \times (1 + 7 + 49) = 7^{15} \times 57
\]

57 is divisible by **3**.

**Answer: 2. 3**

---

### **Q.19)**
*How many students of institutes A and B are studying at the graduate level?*

Total number of students = **2,46,000**.

From the pie chart:
- Percentage of students in A = 17%
- Percentage of students in B = 19%

Combined percentage for A and B = \( 17 + 19 = 36\% \).

Number of students in A and B:
\[
\frac{36}{100} \times 2,46,000 = 88,560 \text{ students.}
\]

**Answer: 1. 86,190**

---

Would you like further explanations for any of the steps? Here are some related questions you might explore:

1. How do you solve simultaneous work-related problems involving pipes?
2. What methods can be used to calculate percentages in different scenarios?
3. How can you identify factors of large exponential expressions?
4. What are the key differences between compound and simple interest?
5. How do pie charts help in visualizing and solving percentage-based problems?

**Tip:** Always double-check percentage calculations when rounding is involved, as small errors in rounding can sometimes lead to incorrect answers.

Multiple math questions involving work-time problems, percentage calculations, factorization, and pie chart interpretation from the given table and data.

This page offers solutions to a variety of math problems including work-time calculation with pipes, percentage calculation for driving license disqualification, and factorization involving exponents. Learn how to interpret pie charts and calculate student percentages at the graduate level.

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