In a class, six students named P, Q, R, S, T and U obtain different marks out of total100 marks. The ratio between marks of T and S is 2: 3 respectively. P obtains 50%marks. R obtains 5 marks less than P. U obtains 1.5 times of the marks obtained by P. T obtains less marks U but more marks than R. Q obtains 20 marks more than T. The ratio between marks of T and U is 4: 5 respectively.

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

I. S obtains 90% marks which are the highest among all.

II. The ratio between marks of P and Q is 5 : 8 respectively.​​

Given: 

In a class, six students named P, Q, R, S, T and U obtain different marks out of total 100 marks.

The ratio between marks of T and S is 2: 3 respectively.

P obtains 50% marks.

R obtains 5 marks less than P.

U obtains 1.5 times of the marks obtained by P.

T obtains less marks U but more marks than R.

Q obtains 20 marks more than T.

The ratio between marks of T and U is 4: 5 respectively.

T : S = 2 : 3

P = 50% of 100 = 50 marks

R = P - 5 = 45 marks

U = 1.5 × P = 1.5 × 50 = 75 marks

T < U but T > R

Q = T + 20

T : U = 4 : 5 → So, T = (4/5) × U = (4/5) × 75 = 60 marks
(Check: 60:75 = 4:5)

P = 50, Q = 80, R = 45, S = 90, T = 60, U = 75

I. S obtains 90% marks which are the highest among all. (True)

II. The ratio between marks of P and Q is 5 : 8 respectively. (True)

So, Both I and II are true.

Thus, correct option is (d).