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CAT 1997 | Question: 107

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A student gets an aggregate of 60% marks in five subjects in the ratio $10:9:8:7:6$. If the passing marks are $50$% of the maximum marks and each subjects has the same maximum marks, in how many subjects did he pass the exam?

  1. $2$
  2. $3$
  3. $4$
  4. $5$
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Let the maximum marks of each subject be 100.

So, Total Mark in five subjects = 500.
Student gets 60% aggregate marks i.e. 60% of 500 = 300 marks.

10x + 9x +8x +7x +6x = 300

40x = 300

x = 300/40 = 7.5.
Marks in first subject = 10x = 10 *7.5 = 75.

Marks in second subject = 9x = 9 *7.5 = 67.5

Marks in third subject = 8x = 8 *7.5 = 60.

Marks in fourth subject = 7x = 7 * 7.5 = 52.5

Marks in last subject = 6 *7.5 = 45.
Thus, he passed in 4 subjects.

Option C is the Correct Answer.

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