Solution -
Let,
The marks in each subject = x
Let,
The ratio of marks in History and Sociology = 1:1
H:S = 1:1 ------------ (1)
The ratio of marks in Sociology and Geography = 2:3
S:G = 2:3 ------------ (2)
The ratio of marks in History and Philosophy = 1:2
H:P = 1:2 ------------ (3)
He has aggregate percentage scored = 55%.
Now,
Multiplying equation (1) by 2 because in equation (2) it is given that marks of Sociology is 2.
So,
H:S = 2(1:1)
H:S = 2:2 ------------ (4)
Now,
Multiplying equation (3) by 2 because in equation (4) it is given that marks of History is 2.
So,
H:P = 2(1:2)
H:P = 2:4 ------------ (5)
Now,
According to eq. (2), (4), (5)
H : S : G : P = 2 : 2 : 3 : 4
As we know,
The marks in each subject = x
Therefore,
The marks in each subject = 2x, 2x, 3x, 4x
Total Marks = 2x + 2x + 3x + 4x
Total Marks = 11x
Aggregate percentage = Total marks / Total No. of subjects
Aggregate percentage = 11x / 4
Aggregate percentage = 55 (given)
11x / 4 = 55
x = 20
Now,
Marks in History = 2x
= 2 * 20
= 40
Marks in Sociology = 2x
= 2 * 20
= 40
Marks in Geography = 3x
= 3 * 20
= 60
Marks in Philosophy = 4x
= 4 * 20
= 80
Therefore,
He score equal to or greater than 60% marks in Geography and Philosophy.
Hence,
The corect answer is option (b) 2.
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