The average age of a group of boys is 18 years and that of girls is 16 years. The average age of the class is 16.4 years. Find the maximum number of boys in the class given that the strength of class is a two digit number.
Answers
Answer:
The maximum no. of boys is 12
Step-by-step explanation:
Formula used:
Average = Sum of all observations/ No. of observations
Sum of all observations = Average * No. of observations
Let no. of boys = a
Let no. of girls = b
Average age of boys = 18
Average age of girls = 16
Average age of class = 16.4
As the strength of the class is a two-digit number, the maximum number of students can be 99.
Assuming there are 99 students, the total age of all students
= 99 * 16.4
= 1623.6
Sum of ages of boys = 18a
Sum of ages of girls = 16b
Sum of ages of all students = 18a + 16b
Hence, we have:
18a + 16b < 1623.6 ....(i)
Also,
a+b < 100 ..(ii) (maximum of students is 99)
Using (ii) in (i), we get:
18a + 16(100 - a) < 1623.6
18a + 1600 - 16a < 1623.6
2a < 1623.6 - 1600
2a < 23.6
a < 12
There can be a maximum of 12 boys in the class