Question

Average marks of 20 students is 45. The average marks of first 10 students is 50 and last 9 students is 40.What is the marks of eleventh student

Answer 1

Answer:

The marks of eleventh student is 40 .

Step-by-step explanation:

We are given that Average marks of 20 students is 45.

So, $Average = \frac{\text{Sum of all marks}}{\text{Total students}}$

$45 = \frac{\text{Sum of  marks of 20 students}}{20}$

$45 \times 20  = \text{Sum of  marks of 20 students}$

$900 = \text{Sum of  marks of 20 students}$

The average marks of first 10 students is 50

$50 = \frac{\text{Sum of  marks of first 10 students}}{10}$

$50 \times 10  = \text{Sum of  marks of first 10 students}$

$500 = \text{Sum of  marks of first 10 students}$

The average of last 9 students is 40

$40 = \frac{\text{Sum of  marks of last 9 students}}{9}$

$40 \times 9 = \text{Sum of  marks of last 9 students}$

$360 = \text{Sum of  marks of last 9 students}$

Sum of marks of first 10 and last 9 students = 500+360= 860

let x be the marks of 11th students

So, Sum of marks of first 10 and last 9 students + marks of 11 th student = Total marks of 20 students

So, $860+x=900$

 $x=900-860$

 $x=40$

Hence the marks of eleventh student is 40 .