10 girls have their average age 14 year and 12 boys have their average age as 16 years . when 6 boys from these 12 join tha 10 girls,they all together have average age as 14.5 year .what is tha average age of tha remaining 6 boys.
To solve this problem, we need to use the concept of average age and make some calculations.
Let's start by finding the total age of the girls. We know that the average age of the 10 girls is 14, so the total age of the girls can be found by multiplying the average age (14) by the number of girls (10): total age of the girls = 14 * 10 = 140.
Similarly, we can find the total age of the boys before 6 of them join the girls. The average age of the 12 boys is given as 16, so the total age of the boys can be found by multiplying the average age (16) by the number of boys (12): total age of the boys = 16 * 12 = 192.
Now, let's consider the scenario where 6 boys join the girls. The total number of people is now 10 girls + 6 boys = 16. The average age of this group is given as 14.5.
We can find the total age of this group by multiplying the average age (14.5) by the number of people (16): total age of the group = 14.5 * 16 = 232.
To find the age of the remaining 6 boys, we can subtract the total age of the girls (140) from the total age of the group (232): age of the remaining 6 boys = total age of the group - total age of the girls = 232 - 140 = 92.
Finally, we can find the average age of the remaining 6 boys by dividing their total age (92) by the number of boys (6): average age of the remaining 6 boys = 92 / 6 = 15.33 years (rounded to two decimal places).
Therefore, the average age of the remaining 6 boys is approximately 15.33 years.