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Here are the solutions to the given questions:

**Q8.** Proteins: \( 12\% \), Fats: \( 25\% \), Carbohydrates: \( 63\% \)

Total daily intake: 2600 calories
- Proteins: \( 12\% \times 2600 = 312 \) calories
- Fats: \( 25\% \times 2600 = 650 \) calories
- Carbohydrates: \( 63\% \times 2600 = 1638 \) calories

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**Q9.** Total runs = 62, Total balls = 96  
Breakdown: 3 sixes, 8 fours, 2 twos, 8 singles.

Percentage of runs:
- Sixes: \( \frac{3 \times 6}{62} \times 100 = 29.03\% \)
- Fours: \( \frac{8 \times 4}{62} \times 100 = 51.61\% \)
- Twos: \( \frac{2 \times 2}{62} \times 100 = 6.45\% \)
- Singles: \( \frac{8 \times 1}{62} \times 100 = 12.90\% \)

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**Q10.** Total runs = 120, Total balls = 150
Breakdown:  
- 6's: \( 20\% \times 120 = 24 \) runs
- 4's: \( 30\% \times 120 = 36 \) runs
- 2's: \( 25\% \times 120 = 30 \) runs
- Singles: \( 25\% \times 120 = 30 \) runs

Percentage of shots that are singles = \( \frac{30}{150} \times 100 = 20\% \)

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**Q11.** Radha earns 22% of her investment as Rs 187.
Let investment be \( x \).  
\( 22\% \times x = 187 \Rightarrow x = \frac{187}{0.22} = Rs 850 \)

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**Q12.** Rohit deposited Rs 1440, which is 12% of his income.
Let income be \( x \).  
\( 12\% \times x = 1440 \Rightarrow x = \frac{1440}{0.12} = Rs 12000 \)

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**Q13.** Gunpowder contains 75% nitre and 10% sulphur.
Total mass of gunpowder = 9 kg  
- Mass of sulphur = \( 10\% \times 9 = 0.9 \) kg  
For 2.3 kg sulphur:  
Total gunpowder required = \( \frac{2.3}{0.1} = 23 \) kg

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**Q14.** 15 parts tin, 105 parts copper (total 120 parts).
Percentage of copper:  
\( \frac{105}{120} \times 100 = 87.5\% \)

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**Q15.** Alloy: 32% copper, 40% nickel, rest zinc.
For 1 kg alloy:  
- Zinc = \( 100\% - 32\% - 40\% = 28\% \)  
Mass of zinc = \( 0.28 \times 1 = 0.28 \) kg

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**Q16.** Traveled 122 km, which is 10% of total journey.
Total journey = \( \frac{122}{0.1} = 1220 \) km

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**Q17.** Total students = 300, Boys = 142, Teachers = 30 (12 are men).
Females = \( 300 + 30 - 142 - 12 = 176 \)
Percentage of females:  
\( \frac{176}{330} \times 100 = 53.33\% \)

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**Q18.** Aman’s income is 20% less than Anil's.
Let Anil's income be \( x \).  
Aman’s income = \( 0.8x \)  
Percentage difference = \( \frac{x - 0.8x}{0.8x} \times 100 = 25\% \)

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**Q19.** Machine depreciates by 5% annually.  
Initial value = Rs 100000  
After 2 years:  
Value = \( 100000 \times (1 - 0.05)^2 = 100000 \times 0.9025 = Rs 90250 \)

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**Q20.** Town population = 60000, Growth rate = 10%.
After 2 years:  
Population = \( 60000 \times (1 + 0.10)^2 = 60000 \times 1.21 = 72600 \)

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**Q21.** Population = 22000, Growth rate = 10%.
After 2 years:  
Population = \( 22000 \times 1.1^2 = 22000 \times 1.21 = 26620 \)  
1 year ago:  
Population = \( \frac{22000}{1.1} = 20000 \)

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**Q22.** Ankit’s new salary = Rs 3575, Increment = 10%.
Old salary = \( \frac{3575}{1.1} = Rs 3250 \)

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Let me know if you'd like any more explanations or further details. Here are some additional practice questions based on this information:

1. How much would Ankit's salary be after a 15% increment from Rs 3250?
2. What is the percentage increase in population after 5 years with a 10% annual growth rate?
3. If a diet contains 15% proteins, how many calories of proteins are there in a 3000-calorie meal?
4. How many runs would a cricketer score if 40% of his total runs came from 6's and his total runs were 80?
5. If a machine depreciates by 8% annually, what would its value be after 3 years if it starts at Rs 80000?

**Tip:** When dealing with percentages, always express the percentage as a decimal (e.g., 12% = 0.12) for easier calculations.

Mathematics for Class VIII - A variety of percentage-based problems ranging from balanced diets, cricket scores, investments, machine depreciation, and population growth calculations.

Explore a series of math problems for Class VIII involving percentages, simple interest, depreciation, and population growth. These problems help in understanding percentage breakdowns, investment calculations, and population trends, suitable for middle school students.

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