Six students A, B, C, D, E, and F appeared for a test of 200 marks. C scored 50\% marks, which is 25\% more than the marks obtained by E. The ratio of marks obtained by A, B, and F is 12:8:9 respectively. D scored 62.5\% more marks than E. It is also given that E and B scored equal marks.

Who scored the highest marks among the six students?

Question

Six students A, B, C, D, E, and F appeared for a test of 200 marks. C scored 50\% marks, which is 25\% more than the marks obtained by E. The ratio of marks obtained by A, B, and F is 12:8:9 respectively. D scored 62.5\% more marks than E. It is also given that E and B scored equal marks.

Who scored the highest marks among the six students?

Accepted Answer

**Solution:**

1. Total marks = 200.

2. C scored 50\% marks, so marks of C = $$ 50\% \times 200 = 100 $$.

3. C's marks are 25\% more than E's marks. Let E's marks be $ x $.

Then, $ $100 = x + 25\% \text{ of } x = x + 0.25x = 1.25x $$.

So, $$ x = \frac{100}{1.25} = 80 $$.

Therefore, E scored 80 marks.

4. Since E and B scored equal marks, B also scored 80 marks.

5. The ratio of marks of A, B, and F is 12:8:9.

Given B's marks = 80, which corresponds to ratio part 8.

So, one part = $$ \frac{80}{8} = 10$ $.

Therefore,

- A's marks = $ $12 \times 10 = 120 $$

- F's marks = $$ 9 \times 10 = 90 $$

6. D scored 62.5\% more than E.

So, D's marks = $ $80 + 62.5\% \text{ of } 80 = 80 + 0.625 \times 80 = 80 + 50 = 130$ $.

7. Now, comparing all marks:

- A = 120

- B = 80

- C = 100

- D = 130

- E = 80

- F = 90

8. Highest marks are scored by D (130).

**Answer:** D

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