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Question

Marks of five students Brijesh, Paresh, Ramesh, Naresh and Suresh in an examination are distinct. Marks of Brijesh is the average of the marks of all these students. Marks of Naresh is the average of the marks of Paresh and Ramesh. Marks of Paresh is the least and marks of Naresh is more than the marks of Suresh. Who got the highest marks?

The correct answer is
Ramesh

Let's analyze the question to determine who got the highest marks among Brijesh, Paresh, Ramesh, Naresh, and Suresh.

  1. It's given that all five students have distinct marks.
  2. The marks of Brijesh are the average of all the students' marks. This implies: \(B = \frac{P + R + N + S + B}{5}\) Simplifying this gives: \(5B = P + R + N + S + B\) \(4B = P + R + N + S\)
  3. The marks of Naresh are the average of the marks of Paresh and Ramesh: \(N = \frac{P + R}{2}\) Hence, \(2N = P + R\)
  4. Paresh has the least marks, so \(P\) is the smallest.
  5. It's stated that Naresh has more marks than Suresh: \(N > S\).
  6. By substituting some assumptions and conditions, we will aim to find who has the highest marks. Given that \(P\) is the smallest and \(N > S\), it leaves Brijesh and Ramesh as potential candidates for the highest marks.
  7. However, since Brijesh's marks are the average of all, his marks are dependent on others and hence unlikely to be highest given distinct values.
  8. Ramesh appears not to have any conditions directly linking his marks to others, giving potential for his marks to be high. Since Naresh's marks are the average of Paresh and Ramesh, Ramesh's marks have to be higher than Naresh to satisfy other conditions (like distinct marks).

Thus, from logical deduction based on given conditions, Ramesh has the highest marks.

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Important Questions from Average (Notes)

  1. The average age of a group of boys and girls is 18 years. If the average age of boys is 20 years and that of girls is 15 years, then what is the percentage of boys in the group?
  2. The average of 13 numbers is 8. If each number is multiplied by 7, then what will the new average be:
  3. There are 78 members in group A, 22 members in group B and 34 members in group C. All the members of these groups went to a restaurant. The average amounts spent on each member of groups A, B and C are ₹136, ₹383 and ₹457, respectively. The overall average amount (in ₹) spent per member is:
  4. If the average of p numbers is $q^2$ and that of q numbers is $p^2$, then the average of (p + q) numbers is :
  5. The average of 101 consecutive odd numbers is 303. Find the largest number.
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