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A student on his birthday distributed on an average 5 chocolates per student. If on the arrival of the teacher and the headmaster to whom 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?

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answer is A.

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Detailed Solution

Suppose the number of students in the class = '

x

'.
Given in the question, 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

= 5 x

Therefore
Total number of chocolates distributed = Number of chocolates for students, teachers and headmaster.
Total number of chocolates distributed

= 5 x + 15 + 10

Total number of chocolates distributed

= 5 x + 25

.
We are given the average chocolate distributed per head =

5.5

.
Total strength = number of students

+

teachers

+

headmaster

= x + 1 + 1 = x + 2

.
So, Total number of chocolates distributed = Average chocolate distributed

\times (x + 2)

= 5 x + 25 = 5.5 (x + 2)

= 5 x + 25 = 5.5 x + 11

= 5.5 x - 5 x = 25 - 11

= 0.5 x = 14

= x = \frac{14}{0.5}

= x = 28

Hence the total number of students in the class

= 28

.
Correct option is 1.

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