Question

The average age of 18 students of a class is 15 years. Out of these, the average age of 9 students is 16 years and that of the other 8 students is 14 years. The average age of 18th student is

Answer 1

Here, we have a total 18 students.

Average age of 18 students = 15 years

Average age of 9 students = 16 years

Average age of 8 students = 14 years

$\text{Average =} \dfrac{\text{Sum of all the observations}}{\text{Number of observations}}$

$\Rightarrow \text{Sum of all observations = Average }\times \text{Number of observations} ...... (1)$

For 9 students, average is 16 years. Using above formula from equation (1),  

Sum of age of 9 students = $9 \times 16 = 144 \text{ years}$

Similarly,

For 8 students, average is 14 years.  Using equation (1):

$Sum of age of 8 students = 8 \times 14 =\text{ 112 years}$

For 18 students, average is 15, using equation (1)

Sum of age of 18 students:

$18 \times 15 =\text{Sum of age of 9 students + Sum of age of 8 students + Age of 18th student}$$\Rightarrow 270 = 144 + 112 + \text{Age of 18th student}\\\Rightarrow \text{Age of 18th student}= 270-256\\\Rightarrow \text{Age of 18th student= 14 years}$

So, age of 18th student is 14 years.