Multiple choice

In a class, average height of all students is 'a' cms. Among them, average height of 10 students is 'b' cms and the average height of the remaining students is 'c' cms. Find the number of students in the class. (Here a > c and b > c)

  1. [a(b - c)](a - c)

  2. (b - c)/(a - c)

  3. (b - c)/[10(a - c)]

  4. [10(b - c)]/(a - c)
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D Correct answer
Explanation

Let N be the total students. The sum of heights is a*N. We are given 10*b + (N-10)*c = a*N. Rearranging gives N(a-c) = 10(b-c), so N = 10(b-c)/(a-c).

AI explanation

Let the total number of students be N, where the sum of all heights is aN. The sum of the 10 students' heights is 10b, and the sum of the remaining students (N minus 10) is c(N minus 10). Setting up the equation aN = 10b + c(N minus 10), we distribute and rearrange to get aN minus cN = 10b minus 10c. Factoring out N and 10 gives N(a minus c) = 10(b minus c), so N equals [10(b - c)]/(a - c).

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