7 pupils of average age 12 years leave a class of 25 pupils of average age 14 years . If 6 new pupils of average age 11 years join the class, what is the average age of the pupils in the class?
Let's first find the total age of the 7 pupils who left:
7 x 12 = 84
And the total age of the 25 pupils who remained:
25 x 14 = 350
So the total age of all the pupils before the new ones arrived was:
84 + 350 = 434
Now let's add the age of the 6 new pupils:
6 x 11 = 66
The total age of all the pupils after the new ones arrived is:
434 + 66 = 500
And finally, the average age of all the pupils in the class is:
500 / 31 = 16.13 (rounded to two decimal places)
Therefore, the average age of the pupils in the class is 16.13 years.
To find the average age of the pupils in the class, you need to calculate the total sum of ages and divide it by the total number of pupils.
Step 1: Calculate the total sum of the ages of the pupils who leave the class.
The average age of the seven pupils who leave is 12 years, so the total sum of their ages is 7 * 12 = 84 years.
Step 2: Calculate the total sum of the ages of the pupils who remain in the class.
There are 25 pupils who remain, and their average age is 14 years. So the total sum of their ages is 25 * 14 = 350 years.
Step 3: Calculate the total sum of the ages of the new pupils who join the class.
There are 6 new pupils who join, and their average age is 11 years. So the total sum of their ages is 6 * 11 = 66 years.
Step 4: Calculate the new total sum of the ages in the class.
The new total sum of ages in the class is the sum of the ages of the pupils who remain and the ages of the new pupils who join.
350 + 66 = 416 years.
Step 5: Calculate the new total number of pupils in the class.
The new total number of pupils in the class is the sum of the pupils who remain and the new pupils who join.
25 + 6 = 31 pupils.
Step 6: Calculate the average age of the pupils in the class.
The average age is the total sum of ages divided by the total number of pupils.
416 / 31 = 13.42 years (rounded to two decimal places).
Therefore, the average age of the pupils in the class is approximately 13.42 years.