Study the given passage carefully and answer the questions.

Six students A, B, C, D, E and F participated in a test of 200 marks. C scored 50% marks which are 25% higher than that of E. ratio of marks obtained by A, B and F is 12:8:9 respectively. D scored 62.5% more marks than E. E and B score equal marks.

Who scored highest marks among 6 students?

The correct option is D.

Let us calculate the marks scored by each of the six students (A, B, C, D, E, and F) step-by-step to determine who scored the highest marks.

Step 1: Find the marks scored by C.
The total marks of the test = 200.
C scored 50% of the total marks.

$\text{C's marks}=50\%\text{ of }200=\frac{50}{100}\times 200=100$

Step 2: Find the marks scored by E.
C's marks are 25% higher than that of E.
This means:

$\text{C's marks}=\text{E's marks}\times \left(1+\frac{25}{100}\right)=\text{E's marks}\times 1.25$

$100=\text{E's marks}\times 1.25$

$\text{E's marks}=\frac{100}{1.25}=80$

Step 3: Find the marks scored by B.
It is given that E and B score equal marks.

$\text{B's marks}=\text{E's marks}=80$

Step 4: Find the marks scored by A and F.
The ratio of marks obtained by A, B, and F is 12 : 8 : 9.
Since B's marks correspond to 8 units in the ratio:

$8\text{ units}=80$

$1\text{ unit}=10$

Therefore, we can calculate the marks for A and F:

$\text{A's marks}=12\times 10=120$

$\text{F's marks}=9\times 10=90$

Step 5: Find the marks scored by D.
D scored 62.5% more marks than E.
Note that 62.5% as a fraction is $\frac{62.5}{100}=\frac{5}{8}$.

$\text{D's marks}=\text{E's marks}+\left(62.5\%\text{ of }\text{E's marks}\right)$

$\text{D's marks}=80+\left(\frac{5}{8}\times 80\right)=80+50=130$

Comparison of marks scored by all 6 students:
• A = 120
• B = 80
• C = 100
• D = 130
• E = 80
• F = 90

Comparing these scores, D scored the highest marks (130 marks).