Let's solve each of the questions from Section B step by step.

Section B [2×6=12]

21. Write all rational numbers whose absolute value is 45.

• Rational numbers are numbers that can be expressed as a fraction of two integers. The absolute value of a number is its distance from zero on the number line, ignoring its sign.
• The rational numbers whose absolute value is 45 are $\pm 45$.
• Therefore, the answers are:
  • $45$
  • $-45$

22. If the product of two rational numbers is -916 and one of them is -415, find the other number.

• Let the two rational numbers be $x$ and $-415$. Their product is $-916$.
• So, $x \times -415 = -916$.
• To find $x$, divide both sides of the equation by $-415$: $x = \frac{-916}{-415} = \frac{916}{415} = 2.207 \, \text{(approx)}$

23. Evaluate: $182.3 + 12.65 - 0.23 - 10.71$. $182.3 + 12.65 - 0.23 - 10.71 = 184.01$

24. The sum of two numbers is 99. If one of the numbers exceeds the other by 9, find the numbers.

• Let the two numbers be $x$ and $y$, with $x > y$.
• We have the following equations: $x + y = 99$ $x = y + 9$
• Substitute $x = y + 9$ into the first equation: $(y + 9) + y = 99$ $2y + 9 = 99$ $2y = 90$ $y = 45$
  • Therefore, $x = 45 + 9 = 54$.
• The two numbers are 54 and 45.

OR

One-fifth of a number minus 4 gives 3. Find the number.

• Let the number be $x$.
• The equation is: $\frac{x}{5} - 4 = 3$
  • Add 4 to both sides: $\frac{x}{5} = 7$
  • Multiply both sides by 5: $x = 35$

25. In the given figure, find $\angle A$ and $\angle ACB$.

• Since the figure is not provided, let's consider a basic triangle. Suppose it's a right-angled triangle at $\angle C$. Then, $\angle A + \angle B + \angle C = 180^\circ$. If $\angle B = 90^\circ$, the sum of $\angle A$ and $\angle ACB$ must be 90 degrees. Further details would require the figure.

26. The mean of 6 observations is 30. If one number is excluded, their mean is 28. Find the excluded observation.

• The sum of the 6 observations is: $6 \times 30 = 180$
• After excluding one number, the sum of the remaining 5 numbers is: $5 \times 28 = 140$
• The excluded number is: $180 - 140 = 40$

OR

The mean of three numbers is 40. Two numbers are 32 and 54. Find the third number.

• Let the third number be $x$.
• The mean of the three numbers is: $\frac{32 + 54 + x}{3} = 40$
  • Multiply both sides by 3: $32 + 54 + x = 120$
  • Simplify: $86 + x = 120$ $x = 34$

These are the solutions to Section B.

Do you want more details or explanations on any of these problems? Here are some related questions for further practice:

1. Solve for the absolute value of a number.
2. Find the product of two rational numbers if their product is given.
3. Evaluate expressions involving decimals.
4. Solve word problems involving the sum and difference of numbers.
5. Find the mean of a given set of observations.

Tip: When working with rational numbers, always simplify fractions and check for common factors.