A student obtained equal marks in History and Sociology. The ratio of marks in Sociology

Ques - 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 he score equal to or greater than 60% marks?

A. 1

B. 2

C. 3

D. none of these 

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.

Thank You