Question

Total marks obtained by P, Q, R and S in Mathematics is 360. How many marks did P secure in Mathematics?
(I) P secured one-third of the total marks of Q, R and S.
(II) Average marks obtained by Q and R are 20 more than that secured by S.

• A. Statement I alone is sufficient to answer the question.
• B. Statement II alone is sufficient to answer the question.
• C. Both statement I and II together are necessary to answer the question.
• D. Both statements I and II together are not sufficient to answer the question.

Hint:

Statement I directly relates P to the rest of the total; solve algebraically.

Answer 1

The Correct Option is A

Method: reason with the ratio between P and the rest of the group instead of full substitution.

1. The total marks are fixed: $P + Q + R + S = 360$.
2. Statement I says P equals one third of the combined marks of Q, R and S. So if the combined marks of Q, R and S is taken as 3 parts, P is 1 part. That makes P exactly 1 part out of a total of 4 parts (1 part P plus 3 parts Q+R+S).
3. Since the 4 parts together equal 360, one part equals $360/4 = 90$. P, being exactly 1 part, equals 90 marks. This is a unique value, so statement I alone answers the question.
4. Statement II only connects Q, R and S to each other ($Q+R = 2S+40$) and never mentions P. Combining it with the total gives $P + 3S = 320$, one equation with two unknowns, so P cannot be pinned down this way.

Because statement I by itself gives a single fixed value for P (90 marks), the answer is option 1: statement I alone is sufficient.

\[\boxed{P = 90,\ \text{Option 1}}\]