Question

Amar wrote exams in four subjects- Physics, chemistry, Biology and Social Studies. The ratio of marks he got in these exams was $ 2:3:4:5. $ He got an aggregate of $ 70\% $ in these exams. Each exam had the same maximum marks. In how many of these exams did he get more than $ 50\% ? $
A. $ 1 $
B. $ 2 $
C. $ 3 $
D. $ 4 $

Answer 1

Hint: First of all we will suppose any variable and will convert the given word statements in the form of mathematical expressions and then will find out the value in form of percentage for the required solution.

Complete step-by-step answer:
Let us consider that the maximum marks of each subject be $ = y $
Let the marks scored in physics be $ = 2x $
In Chemistry be $ = 3x $
In Biology be $ = 4x $
And social studies be $ = 5x $
Now, the total marks scored in all four subjects is $ = 2x + 3x + 4x + 5x = 14x $
Total maximum marks of all four subjects is $ = 4y $
According to the given data:
 $ \left( {\dfrac{{14x}}{{4y}} \times 100} \right)\% = 70\% $
Simplify the above equation –
 $ \Rightarrow \left( {\dfrac{{14x}}{{4y}} \times 25 \times 4} \right) = 70 $
Common factors from the numerator and the denominator cancel each other.
 $ \Rightarrow \left( {\dfrac{{14x}}{y} \times 25} \right) = 70 $
Now, cross multiply the above equation, where the numerator of one side is multiplied with the denominator on the opposite side.
 $ \Rightarrow 14x \times 25 = 70y $
Make “y” the subject. Term multiplicative on one side is moved to the opposite side then it goes to the denominator.
 $ \Rightarrow \dfrac{{14x \times 25}}{{70}} = y $
Common multiples from the numerator and the denominator cancel each other.
 $ \Rightarrow 5x = y $
It can be re-written as –
 $ \Rightarrow y = 5x $
Now the percentage of marks scored in Physics $ = \left( {\dfrac{{2x}}{{5x}} \times 100} \right)\% = 40\% $ ... (A)
The percentage of marks scored in Chemistry $ = \left( {\dfrac{{3x}}{{5x}} \times 100} \right)\% = 60\% $ ... (B)
The percentage of marks scored in Biology $ = \left( {\dfrac{{4x}}{{5x}} \times 100} \right)\% = 80\% $ ... (C)
The percentage of marks scored in Social studies $ = \left( {\dfrac{{5x}}{{5x}} \times 100} \right)\% = 100\% $ ... (D)
From the equations (A), (B), (C) and (D)
Amar scored more than $ 50\% $ in chemistry, Biology and social studies.
So, the correct answer is “Option C”.

Note: Be careful while simplifying equations and always remember the percentage is with respect to hundred. In ratio there is always a common factor among the two quantities if not the ratios are said to be in simplest form. Be careful while converting the given word statements to mathematical expressions since it is the base of the solution.