Six girls named A, B, C, D, E and F score different marks in an examination. B scores more marks than D. The ratio between marks of D and E is 5: 8 respectively. F scores 5 marks more than A. C scores more marks than E. B scores lesser marks than C. The sum of marks obtained by D and E is 130. The ratio between marks of A and D is 11:10 respectively.

Which of the following is true based on the given information?

I. F scores 60 marks.

II. C scores the highest marks.​​

​Six girls named A, B, C, D, E and F score different marks in an examination. B scores more marks than D.

The ratio between marks of D and E is 5: 8 respectively.

F scores 5 marks more than A.

C scores more marks than E.

B scores lesser marks than C.

The sum of marks obtained by D and E is 130.

The ratio between marks of A and D is 11:10 respectively.​​

From D + E = 130 and D : E = 5 : 8:

5 parts + 8 parts = 13 parts

So, 1 part = 130 ÷ 13 = 10

Thus:

D = 5 × 10 = 50 marks

E = 8 × 10 = 80 marks

Given A : D = 11 : 10, and D = 50.

Thus:

A = (11/10) × 50

A = 55 marks

Given F scores 5 marks more than A.

Thus:

F = A + 5, F = 55 + 5

F = 60 marks

​C scores the highest marks among all (because C > E = 80, and B < C).

​I. F scores 60 marks.

True (we found F = 60 marks)

II. C scores the highest marks.
True (C > E and B < C)

Thus, the correct option is: (a)