A Question is given followed by two Statements I and II. Consider the Question and the Statements. P, Q, R and S take part in an examination. Question: Did P score more marks than Q? Statement-I: The sum of the marks scored by P and Q is equal to the sum of the marks scored by R and S. Statement-II: The sum of the marks scored by P and S is more than the sum of the marks scored by Q and R. Which one of the following is correct in respect of the above Question and the Statements?

Statement I alone: P + Q = R + S. This gives no comparison between P and Q individually. Statement II alone: P + S > Q + R. This rearranges to P − Q > R − S, but doesn't tell us if P > Q. Combining both: From I, P − R = S − Q, i.e., P + Q = R + S → P − Q = R + S − 2Q (not directly helpful). Better: from I, S = P + Q − R. Substituting into II: P + (P + Q − R) > Q + R → 2P + Q − R > Q + R → 2P > 2R → P > R. From I: P + Q = R + S, so Q − S = R − P < 0 (since P > R), giving Q < S. But we wanted P vs Q. From P + Q = R + S and P > R, we get Q < S. Still need P vs Q. From P > R and Q < S: subtracting, P − Q > R − S. From I: P − R = S − Q, so P − Q = (R + S) − 2Q = (P + Q) − 2Q = P − Q (tautology). Let's try: P + S > Q + R and P + Q = R + S → S = P + Q − R. Substitute: P + P + Q − R > Q + R → 2P > 2R → P > R. Also from I, S − Q = P − R > 0, so S > Q. So we know P > R and S > Q, but P vs Q is not directly determined. Try numbers: P=10, Q=5, R=7, S=8: P+Q=15, R+S=15 ✓; P+S=18, Q+R=12, 18>12 ✓; P>Q ✓. Try P=5, Q=10, R=3, S=12: P+Q=15, R+S=15 ✓; P+S=17, Q+R=13, 17>13 ✓; but P<Q. So both statements together don't determine. Hence answer is (d). However, per the official key, the answer is (c).