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

Step 1: Write the total.
P + Q + R + S = 360.
Step 2: Use statement I.
Statement I says P = (1/3)(Q + R + S). Since Q + R + S = 360 - P, substitute: P = (360 - P)/3. Multiply both sides by 3: 3P = 360 - P. Add P to both sides: 4P = 360. Divide by 4: P = 90. This gives a unique value of P using only statement I, so statement I alone is sufficient.
Step 3: Use statement II.
Statement II says (Q + R)/2 = S + 20, so Q + R = 2S + 40. This links Q, R and S together but says nothing about P directly. Substituting into the total: P + (2S + 40) + S = 360, which gives P + 3S = 320. This single equation has two unknowns (P and S), so P cannot be pinned to one value. Statement II alone is not sufficient.
Step 4: Conclude.
Statement I alone pins down P = 90 uniquely, while statement II alone leaves P undetermined. So statement I alone is sufficient to answer the question, matching option 1.