Question

The average age of 40 students of a class is 16 years. After admission of 10 new students to the class, the average becomes 15 years. If the average age of 5 of the new students is 11 years, then the average age (in years) of the remaining 5 new students is:

• A. 11
• B. 16
• C. 15
• D. 10

Answer 1

Answer:

A. 11

Solution:

Given:

The average age of 40 students = 16 years

On admission of 10 new students average = 15 years

Average of 5 new students = 11

Formula used:

${\rm{Average}} = \frac{{{\rm{sum\;of\;all\;the\;values}}}}{{{\rm{number\;of\;values}}}}$

Calculation:

Sum of all ages of 40 students =$40\times{16}$

⇒ 640 years

After admission of 10 new students, number of students now = 40 + 10

⇒ 50

Sum of all ages after the admission of 10 new students = $50\times{15}$

⇒ 750 years

Sum of ages of 5 new students = $5\times{11}$

⇒ 55 years

Now remaining ages of 5 new students = Sum of all ages after the admission of 10 new students - Sum of all ages of 40 students - Sum of ages of 5 new students

⇒ 750 – 640 – 55

⇒ 750 – 695

⇒ 55 years

Average of 5 new students =$\frac{55}{5}$

⇒ 11

Hence, the Average of 5 new students is 11.