Question

In a class of 10 students, the average marks obtained by them is 30. the average marks obtained by the first six students is 20, and the last five is 42. find the marks obtained by the sixth student.

Answer 1

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Answer 2

Answer:

30

Step-by-step explanation:

Mean of 10 students = $\frac{\text{sum of marks of 10 students}}{\text{Total no. of students}}$

$30=\frac{\text{sum of marks of 10 students}}{10}$

$300=\text{Sum of marks of 10 students}$ --A

Let the 10 students be a,b,c,d,e,f,g,h,i,j

Now Mean of first six students = $\frac{\text{sum of marks of first 6 students}}{\text{No. of students}}$

$20=\frac{\text{sum of marks of first 6 students}}{6}$

$120=\text{sum of marks of first 6 students}$--1

Now Mean of last five students = $\frac{\text{sum of marks of last 5 students}}{\text{No. of students}}$

$42=\frac{\text{sum of marks of last 5 students}}{5}$

$210=\text{sum of marks of first 6 students}$--2

Now Add 1 and 2

So, 210+120=No. of first 6 students +no. of last five students

330=(a+b+c+d+e+f) +(f+g+h+i+j)

330=a+b+c+d+e+f+f+g+h+i+j

Using A

330=300+f

So, 30 = f

Thus the marks obtained by sixth student is 30.