Question

The average weight of 15 students in a group is 26 kg. When the teacher's
weight is included it becomes 30 kg. What is the weight of the teacher?
A) 78
B) 86
C) 62
D) 90​

Answer 1

GIVEN :-

• The average weight of 15 students in a group is 26kg.
• When teacher's weight is included , it becomes 30kg.

TO FIND :-

• Weight of the teacher.

SOLUTION :-

Average of 15 students is 26kg.

Let the sum of weight of all students be 'x'.

So,

$\\ \boxed{ \sf \: average = \dfrac{sum \: of \: all \: numbers}{total \: numbers} } \\ \\ \implies\sf \: 26 = \dfrac{x}{15} \\ \\ \implies \sf \: x = 26 \times 15 \\ \\ \implies \underbrace{\sf \: x = 390}$

Now , for average of students and teacher .

Let the weight of teacher be 'y'.

♦ Total members

= 15(students) + 1(teacher)

= 16

♦ Total weight

= x(students) + y(teacher)

= x + y

♦ We are given that average is 30kg.

So,

$\\ \implies \sf \: 30 = \dfrac{x + y}{16} \\ \\ \implies \sf \: 480 = x + y$

Putting value of x=390,

$\\ \sf \implies \: 480 = 390 + y \\ \\ \sf \implies \: y = 480 - 390 \\ \\ \implies \underbrace{ \sf \: y = 90}$

Hence , weight of teacher is 90kg.