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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Question : The average of the first three numbers is double the fourth number. If the average of all the four numbers is 12. Find the 4th number.
Option 1: $16$
Option 2: $\frac{48}{7}$
Option 3: $20$
Option 4: $\frac{18}{7}$
Question : The average age of 30 students in a class is 14 years, 4 months. After the admission of five new students in the class, the average becomes 13 years and 9 months. The youngest of the five new students is 9 years and 11 months old. The average age of the remaining four new students is:
Option 1: 11 years 2 months
Option 2: 13 years 6 months
Option 3: 12 years 4 months
Option 4: 10 years 4 months
Question : The sum of three consecutive even numbers is 28 more than the average of these three numbers. Then the smallest of these three numbers is:
Option 1: 6
Option 2: 12
Option 3: 14
Option 4: 16
Question : The current ages of Sudhir and Ashish are in the ratio 5 : 7. Twelve years ago, the ratio of their ages was 1 : 2. What will be the age of Sudhir five years from now?
Option 2: 25 years
Option 3: 33 years
Option 4: 28 years
Question : Ravi is 12 years younger than Surya. Ravi's age is 40% of the sum of his and Surya's ages. What will be Surya's age 9 years from now?
Option 1: 36
Option 2: 24
Option 3: 33
Option 4: 45
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