Question : The average age of 7 students in a class is 28 years. The average age of the first three students is 30 years. The age of the fourth student is 4 years less than the age of the fifth student. The ages of the last two students are the same and are 5 more than the average age of the first three students. What is the average age of fourth and fifth students?
Option 1: 20 years
Option 2: 36 years
Option 3: 16 years
Option 4: 18 years
Correct Answer: 18 years
Solution :
Given: The average age of 7 students in a class is 28 years.
$\text{Average}=\frac{\text{The sum of ages}}{\text{The number of students}}$
Let the sum of the ages of the first 3 students be $x$.
⇒ $\frac{x}{3}=30$
⇒ $x=90$
Let the ages of the fourth and fifth students be $y$ and $z$ respectively.
⇒ $y=z–4$
Let the ages of the last two students be $p$ and $q$ respectively.
⇒ $p=q=30+5=35$
According to the question,
$\frac{x+y+z+p+q}{7}=28$ (equation 1)
Substitute the values in the equation 1,
⇒ $\frac{90+z–4+z+35+35}{7}=28$
⇒ $\frac{156+2z}{7}=28$
⇒ $156+2z=196$
⇒ $2z=40$
⇒ $z=20$ years
The age of the fourth student = $y$ = 20 – 4 = 16 years.
The average age of fourth and fifth students = $\frac{y+z}{2}=\frac{16+20}{2}=\frac{36}{2}=18$ years
Hence, the correct answer is 18 years.
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