Question

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

Answer 1

Hint: Using the concept of Ratio and Proportion, this question can be solved. Initially, assume that the ratio of marks in History and Sociology be 1:1 and also assume that the marks in each subject be ‘x’. Now, find out the proportion of History: Sociology: Geography: Philosophy. Then, write down the marks in each subject in terms of ‘x’.
Then, find out the total marks by summing the marks of History, Sociology, Geography and Philosophy. As, it is mentioned that maximum marks in each subject are equal, then find out the aggregate percentage by using average concept. As, the aggregate percentage is given as 55% marks. Now, make the average value equal to the aggregate percentage in order to calculate the value of ‘x’.
Finally, substitute the value of ‘x’ in each subject to check out the number of subjects in which student scores equal to or greater than 60% marks.

Complete step-by-step answer:
Let the ratio of marks in History and Sociology be 1:1, and it can be denoted as:
$\Rightarrow$ \[H:S\to 1:1----(1)\]
Let the marks in each subject be \textit{`x'}.
It is given that:
The ratio of marks in Sociology and Geography = 2: 3, and let it be denoted as:
$\Rightarrow$ \[S:G\to 2:3----(2)\]
The ratio of marks in History and Philosophy = 1: 2, and let it be denoted as:
$\Rightarrow$ \[H:P\to 1:2----(3)\]
The aggregate percentage scored by students = 55\%.
To find: The number of subjects in which student scores equal to or greater than 60\% marks.
Now, multiplying equation ‘1’ by '2' because in equation ‘2’ it is very clearly given that marks in Sociology is `2' and, we get:
$\Rightarrow$ \[H:S\to 2:2----(4)\]
Now, as it clear from equation ‘4’ that marks in History is `2', so multiply equation ‘3’ by '2' and we get:
$\Rightarrow$ \[H:P\to 2:4----(5)\]
Now, by using equation ‘2’ , ‘4’ and ‘5’, we get:
$\Rightarrow$ \[H:S:G:P\to 2:2:3:\ 4\]
Therefore, the marks in subjects are 2x, 2x, 3x and 4x.
Total marks will be calculated by:
$\Rightarrow$ \[Total\ Marks=\ H+S+G+P\ =2x+2x+3x+4x\]
$\Rightarrow$ \[ Total\ Marks=11x\]
Maximum marks in each subject are equal.
\[\therefore Aggregate\%\ =\ \dfrac{Total\ Marks}{Total\ Number\ of\ Subjects}\]
$\Rightarrow$ \[ Aggregate\%\ =\ \dfrac{11x}{4}\]
$\Rightarrow$ \[ 55\ =\ \dfrac{11x}{4}\Rightarrow \left(55\times 4\right)=11x\Rightarrow 220\ \ =11x\]
$\Rightarrow$ \[ x=20\]
Therefore,
Marks in History = $2x\ =2\times 20\ =40$,
Marks in Sociology = $2x\ =2\times 20\ =40$,
Marks in Geography = $3x\ =3\times 20\ =60$ and
Marks in Philosophy = $4x\ =4\times 20\ =80$.
Thus, in two subjects he scored more than equal to 60%.

Hence, the correct option is B

Note:
Always for such questions try to find out the proportion first and then assume that the marks in each subject be ‘x’. Then, find out the total marks by summing the marks of the mentioned subject. Finally, find out the aggregate percentage by using the average concept to find the value of ‘x’.