To explain the solution shown in the first image for the question in the second image, let’s break down the process:

Problem Recap (from the second image):

A student has equal marks in History (H) and Sociology (S). The ratio of marks in Sociology and Geography (G) is $2:3$, and the ratio of marks in History and Philosophy (P) is $1:2$. The student scored an aggregate of 45% across these subjects. The task is to determine in how many subjects the student scored 60% or more.

Solution Steps (from the first image):

1. Given Ratios:

   • $H : S = 1 : 1$
   • $S : G = 2 : 3$
   • $H : P = 1 : 2$

2. Combining the Ratios:

   • From $H : S = 1 : 1$, we know $H = S$.
   • $S : G = 2 : 3$ implies that if $S = 2x$, then $G = 3x$.
   • $H : P = 1 : 2$ implies that if $H = x$, then $P = 2x$.
   • Therefore, $H : S : G : P = 2x : 2x : 3x : 4x$.

3. Total Marks and Aggregate:

   • The total marks in all subjects is $2x + 2x + 3x + 4x = 11x$.
   • Given that the aggregate score is 45%, we have: $\frac{11x}{4} = \frac{45}{100} \times 4 \times 100 \text{ (since each subject has equal maximum marks)}$
   • Therefore, $x$ is found to be 20.

4. Calculating Individual Marks:

   • $H = 2x = 40$
   • $S = 2x = 40$
   • $G = 3x = 60$
   • $P = 4x = 80$

5. Subjects with Marks ≥ 60%:

   • Geography (G): 60 marks.
   • Philosophy (P): 80 marks.
   • So, there are 2 subjects where the student scored 60% or more.

Final Answer:

Thus, the student scored 60% or more in 2 subjects. Hence, the correct answer to the question in the second image is (b) 2.

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Would you like more details or have any questions?

Here are some related questions you might find helpful:

1. How do you combine ratios involving different quantities?
2. Why is it necessary to normalize the ratios before solving the problem?
3. How is the aggregate score calculation applied in different scenarios?
4. How can you determine the individual marks from given ratios and totals?
5. What steps should be taken to check the accuracy of ratio-based problems?
6. How do you solve ratio problems when additional subjects are introduced?
7. What would be the impact if one subject had a different maximum mark?
8. How to interpret percentage scores when the total possible marks vary?

Tip: When dealing with ratio problems, always ensure the ratios are consistently scaled before performing any calculations to avoid errors.