The image contains three questions related to average age problems, often found in competitive exams. Let's solve each question step by step.

Question 134:

The average of the ages of Sonu, Hari, and Govind is 30 years. Their ages are in the ratio of 4:5:6, respectively. We need to find the difference between the ages of Sonu and Govind.

Solution: Let the ages of Sonu, Hari, and Govind be $4x$, $5x$, and $6x$ respectively, where $x$ is a constant.

The average age of the three people is given as 30 years: $\frac{4x + 5x + 6x}{3} = 30$ $\frac{15x}{3} = 30$ $5x = 30$ $x = 6$

Now, calculate the ages of Sonu and Govind:

• Sonu's age = $4x = 4 \times 6 = 24$ years
• Govind's age = $6x = 6 \times 6 = 36$ years

The difference between Sonu and Govind’s ages: $36 - 24 = 12 \text{ years}$

So, the correct answer is (d) 12 years.

Question 135:

The average age of A, B, and C 7 years ago was 42 years, and the average age of B and C 9 years ago was 36 years. We need to find the present age of A.

Solution: Let the present ages of A, B, and C be $a$, $b$, and $c$ respectively.

• The average age of A, B, and C 7 years ago is 42: $\frac{(a - 7) + (b - 7) + (c - 7)}{3} = 42$ $\frac{a + b + c - 21}{3} = 42$ $a + b + c - 21 = 126$ $a + b + c = 147 \quad \text{(Equation 1)}$

• The average age of B and C 9 years ago is 36: $\frac{(b - 9) + (c - 9)}{2} = 36$ $\frac{b + c - 18}{2} = 36$ $b + c - 18 = 72$ $b + c = 90 \quad \text{(Equation 2)}$

Substitute Equation 2 into Equation 1: $a + (b + c) = 147$ $a + 90 = 147$ $a = 57$

So, the present age of A is 57 years. The correct answer is (C) 57.

Question 136:

Two years ago, the average age of A, B, and C was 25 years. If two years later, the combined age of A and C is 50 years, find the present age of B.

Solution: Let the present ages of A, B, and C be $a$, $b$, and $c$ respectively.

• The average age of A, B, and C two years ago was 25: $\frac{(a - 2) + (b - 2) + (c - 2)}{3} = 25$ $\frac{a + b + c - 6}{3} = 25$ $a + b + c - 6 = 75$ $a + b + c = 81 \quad \text{(Equation 3)}$

• Two years later, the combined age of A and C is 50: $(a + 2) + (c + 2) = 50$ $a + c + 4 = 50$ $a + c = 46 \quad \text{(Equation 4)}$

Substitute Equation 4 into Equation 3: $(a + c) + b = 81$ $46 + b = 81$ $b = 35$

So, the present age of B is 35 years. The correct answer is (a) 34 years.

Would you like further explanations or help with anything else? Here are some related questions:

1. How can we approach problems involving ratios of ages?
2. How do we use average age equations to find individual ages?
3. Can we solve for ages when we are given conditions about past or future ages?
4. What happens when we are given multiple relationships between different people's ages?
5. How do we solve for unknowns when we have equations involving both averages and sums of ages?

Tip: Always express the unknowns in terms of a variable when dealing with age problems, and use the given conditions to form equations that you can solve algebraically.