Question

A student on his birthday distributed an average 5 chocolates per student. If on the arrival of the teacher and the headmaster to when the student gives 10 and 15 chocolates respectively, the average chocolate distributed per head increases to 5.5, then what is the number of students in the class?
(a) 28
(b) 30
(c) 32
(d) 36

Answer 1

Hint: Take ‘x’ as the number of students. Find the total number of chocolates distributed by adding the number of chocolates distributed to students, teacher and headmaster. Total strength is (x + 2) including the students, teacher and headmaster. Then use the concept of average, where we divide the sum of all data by the total number of data. Thus the total number of chocolates distributed are equal to the product of distribution and (x + 2). Solve and find x.

Complete step-by-step answer:
Let us consider the number of students in the class as ‘x’. The students distribute an average of 5 chocolates per student.
Number of chocolates to the teacher = 10
Number of chocolates for the headmaster = 15
Number of chocolates given to x students = 5x
\[\therefore \] Total number of chocolates distributed = Number of chocolates for students, teachers and headmaster.
\[\therefore \] Total number of chocolates distributed = 5x + 15 + 10 = 5x + 25.
We are given the average chocolate distributed per head as 5.5.
Total strength = number of students + teachers + headmaster = x + 1 + 1 = x + 2.
\[\therefore \] Total number of chocolate distributed = Average chocolate distributed \[\times \] (x + 2).
\[\Rightarrow 5x+25=5.5\left( x+2 \right)\]
Let us simplify the above expression and find the value of x.
\[\begin{align}
  & \Rightarrow 5x+25=5.5x+11 \\
 & \Rightarrow 5.5x-5x=25-11 \\
 & \Rightarrow 0.5x=14 \\
 & \therefore x=\dfrac{14}{0.5}=28 \\
\end{align}\]
Hence the total number of students in the class = 28.
\[\therefore \] Option (a) is the correct answer.

Note: Remember that the total number of chocolates distributed are equal to the average chocolate distribution and total strength. This is one of the key points to keep in mind while solving such questions.