Ratio and Proportion: A student obtained equal marks in History and Sociology. The ratio of marks in Sociology and Geography is 2 : 3 and the ratio of marks in History and Philosophy is 1 : 2. If he has scored an aggregate of 55% marks. The maximum marks in each subject is the same. In how many subjects did his Score equal to or greater than 60% marks?

Step 1: Let the marks in History and Sociology be x

Given:

History = x

Sociology = x

Sociology : Geography = 2 : 3 → Geography = (3/2)x

History : Philosophy = 1 : 2 → Philosophy = 2x

So, marks in 5 subjects:

History = x

Sociology = x

Geography = (3/2)x

Philosophy = 2x

Total marks = x + x + (3/2)x + 2x = (6.5)x

Step 2: Use aggregate percentage

Aggregate = 55% Let maximum marks per subject = 100 → total max = 5 × 100 = 500 So total marks scored = 55% of 500 = 275

Now set up the equation: (6.5)x = 275 → x = 275 / 6.5 = 42.31

Step 3: Calculate marks in each subject

History = 42.31

Sociology = 42.31

Geography = (3/2) × 42.31 = 63.47

Philosophy = 2 × 42.31 = 84.62

Step 4: Check subjects with ≥ 60%

60% of 100 = 60 marks Subjects with ≥ 60 marks:

Geography = 63.47 ✅

Philosophy = 84.62 ✅