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 marks of the total of Q, R and S.
(II) Average marks obtained by Q and R are 20 more than that secured by S.
(I) P secured one-third marks of the total of Q, R and S.
(II) Average marks obtained by Q and R are 20 more than that secured by S.
- Statement I alone is sufficient to answer the question.
- Statement II alone is sufficient to answer the question.
- Both statements I and II together are necessary to answer the question.
- Both statements I and II together are not sufficient to answer the question.
The Correct Option is A
Solution and Explanation
Total marks obtained by P, Q, R, and S in Mathematics is 360. We need to find out the marks secured by P.
Statement I: P secured one-third marks of the total of Q, R, and S.
Let marks secured by P be \( x \). Then marks secured by Q, R, and S together are \( 360-x \). According to the statement: \( x = \frac{1}{3}(360-x) \). Solving this equation:
\( x = \frac{1}{3}(360-x) \)
\( x = 120 - \frac{x}{3} \)
\( 3x + x = 360 \)
\( 4x = 360 \)
\( x = 90 \)
Therefore, P secured 90 marks. Statement I is sufficient.
Statement II: Average marks obtained by Q and R are 20 more than that secured by S.
This gives us: \( \frac{Q+R}{2} = S+20 \). This equation alone does not help us to calculate the exact mark secured by P without additional information. Statement II alone is insufficient.
Therefore, the answer is that Statement I alone is sufficient to answer the question.
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