Exam Marks Proportion

CAT 2001 Slot 1 · QA · Easy · Ratio and Proportion

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A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6:7:8:9:106 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60%60\% of the total marks. Then the number of papers in which he got more than 50%50\% marks is:

  1. A.

    2

  2. B.

    3

  3. C.

    4

  4. D.

    5

Answer

C

Explanation

Let the full marks for each paper be 100. Total full marks = 500. Total marks obtained = 60%60\% of 500=300500 = 300. The marks in 5 papers are in ratio 6x:7x:8x:9x:10x6x : 7x : 8x : 9x : 10x. Sum = 40x=300  ⟹  x=7.540x = 300 \implies x = 7.5. Marks obtained: 6(7.5)=456(7.5) = 45, 7(7.5)=52.57(7.5) = 52.5, 8(7.5)=608(7.5) = 60, 9(7.5)=67.59(7.5) = 67.5, 10(7.5)=7510(7.5) = 75. 50%50\% of full marks is 50. The marks greater than 50 are 52.5, 60, 67.5, and 75, which is in 4 papers.

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