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.

What is ratio of marks obtained by B, D and F?

The correct option is 8 :13 :9.

Let us calculate the marks obtained by each student step-by-step based on the given information:

1. Total Marks of the test: 200 marks.

2. Marks obtained by C:

C scored 50% of the total marks (200).

$\text{Marks of C}=50\%\text{ of }200=\frac{50}{100}\times 200=100$

3. Marks obtained by E:

C's marks are 25% higher than E's marks. This means C scored 125% of E's marks.

$\text{Marks of C}=1.25\times \text{Marks of E}$

$100=\frac{5}{4}\times \text{Marks of E}$

$\text{Marks of E}=\frac{100\times 4}{5}=80$

4. Marks obtained by B:

It is given that E and B score equal marks.

$\text{Marks of B}=\text{Marks of E}=80$

5. Marks obtained by D:

D scored 62.5% more marks than E.

Note that 62.5% is equal to 5/8 in fraction.

$\text{Marks of D}=\text{Marks of E}+(62.5\%\text{ of }\text{Marks of E})$

$\text{Marks of D}=80+(\frac{5}{8}\times 80)=80+50=130$

6. Marks obtained by F:

The ratio of marks obtained by A, B, and F is given as 12 : 8 : 9.

From the ratio, the ratio unit for B corresponds to 8 parts.

Since B scored 80 marks:

$8\text{ parts}=80$

$1\text{ part}=10$

Therefore, the marks obtained by F (which corresponds to 9 parts) is:

$\text{Marks of F}=9\times 10=90$

7. Ratio of marks obtained by B, D, and F:

Now, we take the ratio of the marks of B, D, and F:

$\text{Ratio}=\text{Marks of B}:\text{Marks of D}:\text{Marks of F}$

$\text{Ratio}=80:130:90$

Dividing each value by 10 to simplify:

$\text{Ratio}=8:13:9$

Thus, the ratio of marks obtained by B, D, and F is 8 :13 :9.