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
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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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