Here are the solutions to the math problems: 13. The average mass of 3 girls is 45kg. Two of them weigh 42kg and 47kg. Find the mass of the third girl. 14. Find the L.C.M. 8, 10, 12.

Here are the solutions to the math problems:

13. The average mass of 3 girls is 45kg. Two of them weigh 42kg and 47kg. Find the mass of the third girl.

• Step 1: Calculate the total mass of the three girls. The average mass is the total mass divided by the number of girls.

  $$\text{Total mass} = \text{Average mass} \times \text{Number of girls}$$ $$\text{Total mass} = 45 \text{ kg} \times 3 = 135 \text{ kg}$$

• Step 2: Calculate the combined mass of the two known girls.

  $$\text{Combined mass} = 42 \text{ kg} + 47 \text{ kg} = 89 \text{ kg}$$

• Step 3: Find the mass of the third girl.

  $$\text{Mass of third girl} = \text{Total mass} - \text{Combined mass of two girls}$$ $$\text{Mass of third girl} = 135 \text{ kg} - 89 \text{ kg} = 46 \text{ kg}$$

  The correct option is c.

  $$\boxed{\text{46 kg}}$$

14. Find the L.C.M. 8, 10, 12.

• Step 1: Find the prime factorization of each number.

  $$8 = 2 \times 2 \times 2 = 2^3$$ $$10 = 2 \times 5$$ $$12 = 2 \times 2 \times 3 = 2^2 \times 3$$

• Step 2: Identify the highest power of each prime factor present. The prime factors are 2, 3, and 5. Highest power of 2: $2^3$ (from 8) Highest power of 3: $3^1$ (from 12) Highest power of 5: $5^1$ (from 10)

• Step 3: Multiply these highest powers together to find the L.C.M.

  $$\text{L.C.M.} = 2^3 \times 3^1 \times 5^1 = 8 \times 3 \times 5 = 24 \times 5 = 120$$

  The correct option is a.

  $$\boxed{120}$$

15. Express 28:42 as a fraction in its simplest form.

• Step 1: Write the ratio as a fraction.

  $$28:42 = \frac{28}{42}$$

• Step 2: Find the greatest common divisor (GCD) of the numerator and denominator. Factors of 28: 1, 2, 4, 7, 14, 28 Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 The GCD of 28 and 42 is 14.

• Step 3: Divide both the numerator and the denominator by their GCD.

  $$\frac{28 \div 14}{42 \div 14} = \frac{2}{3}$$

  The correct option is not explicitly listed as a fraction, but 2:3 is equivalent to $\frac{2}{3}$.

  $$\boxed{\frac{2}{3}}$$

16. $3/5 = x/20$. What is x?

• Step 1: Set up the proportion.

  $$\frac{3}{5} = \frac{x}{20}$$

• Step 2: Solve for x by cross-multiplication.

  $$3 \times 20 = 5 \times x$$ $$60 = 5x$$

• Step 3: Divide to find x.

  $$x = \frac{60}{5}$$ $$x = 12$$

  The correct option is e.

  $$\boxed{12}$$

17. Express $7\frac{1}{2}\%$ as a fraction in its simplest form.

• Step 1: Convert the mixed percentage to an improper fraction.

  $$7\frac{1}{2}\% = \frac{7 \times 2 + 1}{2}\% = \frac{15}{2}\%$$

• Step 2: Convert the percentage to a fraction by dividing by 100.

  $$\frac{15}{2}\% = \frac{15}{2 \times 100} = \frac{15}{200}$$

• Step 3: Simplify the fraction. Find the greatest common divisor (GCD) of 15 and 200. Both are divisible by 5.

  $$\frac{15 \div 5}{200 \div 5} = \frac{3}{40}$$

  The correct option is d.

  $$\boxed{\frac{3}{40}}$$

18. Express 0.275 as a percentage.

• Step 1: Multiply the decimal by 100 to convert it to a percentage. $$0.275 \times 100\% = 27.5\%$$ The correct option is a. $$\boxed{27.5\%}$$

19. Express 1291 as a decimal.

• Explanation: The question "Express 1291 as a decimal" typically means to write the integer with a decimal point, which is 1291.0. However, given the options and common question patterns, it's highly probable that the question implicitly means "Express $\frac{1291}{1000}$ as a decimal" or similar. Based on the handwritten work in the image, it seems to imply division by 1000.
• Step 1: Assume the question implies $\frac{1291}{1000}$. $$\frac{1291}{1000} = 1.291$$ The correct option is a. $$\boxed{1.291}$$

20. $1\frac{1}{2} - \frac{1}{3} \times \frac{1}{3}$

• Step 1: Convert the mixed number to an improper fraction.

  $$1\frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2}$$

• Step 2: Perform the multiplication first (following order of operations).

  $$\frac{1}{3} \times \frac{1}{3} = \frac{1 \times 1}{3 \times 3} = \frac{1}{9}$$

• Step 3: Perform the subtraction.

  $$\frac{3}{2} - \frac{1}{9}$$

  Find a common denominator, which is 18.

  $$\frac{3 \times 9}{2 \times 9} - \frac{1 \times 2}{9 \times 2} = \frac{27}{18} - \frac{2}{18}$$ $$\frac{27 - 2}{18} = \frac{25}{18}$$

• Step 4: Convert the improper fraction to a mixed number (optional, but often preferred for final answers).

  $$\frac{25}{18} = 1\frac{7}{18}$$

  The correct option is b, which is $2\frac{47}{50}$ (incorrect) or c, which is $1\frac{1}{4}$ (incorrect). Let's recheck the options. Option 'b' is $2\frac{47}{50}$, option 'c' is $1\frac{1}{4}$, option 'd' is $4/5$, option 'e' is $1\frac{7}{18}$. So 'e' is the correct option.

  $$\boxed{1\frac{7}{18}}$$

21. The marks in a history test are awarded out of 75. If a girl scored 64%, how many marks did she get?

• Step 1: Convert the percentage to a decimal.

  $$64\% = \frac{64}{100} = 0.64$$

• Step 2: Calculate the marks obtained.

  $$\text{Marks obtained} = \text{Percentage score} \times \text{Total marks}$$ $$\text{Marks obtained} = 0.64 \times 75$$ $$\text{Marks obtained} = 48$$

  The correct option is c.

  $$\boxed{48}$$

22. There are 500 pupils in a school. If 275 are boys, what percentage are girls?

• Step 1: Calculate the number of girls.

  $$\text{Number of girls} = \text{Total pupils} - \text{Number of boys}$$ $$\text{Number of girls} = 500 - 275 = 225$$

• Step 2: Calculate the percentage of girls.

  $$\text{Percentage of girls} = \frac{\text{Number of girls}}{\text{Total pupils}} \times 100\%$$ $$\text{Percentage of girls} = \frac{225}{500} \times 100\%$$ $$\text{Percentage of girls} = 0.45 \times 100\% = 45\%$$

  The correct option is c.

  $$\boxed{45\%}$$

**23. A sack containing coconuts weighed 460g. When more coconuts were added the weight was increased by 2