Question

The average age of \[r\] boys in a class is \[a\] years. If the average age of \[s\] of them is \[b\] years, then what is the average age of the remaining boys?
A.\[\dfrac{{ra - sb}}{{r - s}}\]
B.\[\dfrac{{ra + sb}}{{r - s}}\]
C.\[\dfrac{{ra - sb}}{{r + s}}\]
D.None of the above

Answer 1

Hint: To find the average age of the remaining boys we will have to find their total age and their count. To find this we will subtract the total age of \[b\] number of boys from the total age of all the boys to get the total age of the remaining boys. Then we will subtract the number of \[b\] boys from the total \[r\] boys to get the number of the remaining boys. We will then divide their total age from their total number to get the average age of the remaining boys

Complete step-by-step answer:
First we will find the total age of all the \[r\] boys. As their average age is \[a\] years, thus their total age will be \[r \times a = ra\] years. Now the average age of \[s\] boys is \[b\], thus their total age will be \[s \times b = sb\] years.
Now, for the remaining boys, their total age will be the difference of the total age of \[r\] boys and the total age of \[s\] boys, which is given as \[ra - sb\] years.
Also the total number of remaining boys will be the difference of total number of \[r\] boys and the total number of \[s\] boys. Thus, the number of the remaining boys will be \[r - s\] boys.
So, the average age of the remaining boys will be \[\dfrac{{ra - sb}}{{r - s}}\] years.
Hence, option (A) is the correct option.

Note: Here, we could find the number of remaining boys and their ages because they are left out from the total \[r\] number of boys. Thus, we can easily subtract the number of \[s\] number of boys from total to get the remaining number of boys. We did a similar calculation for finding the total age of the remaining boys.