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. Select one: a. 30 b. 35 c. 40 d. 27

Answer 1

$\bf {\huge {\underline {\boxed {\sf\purple {Answer:\:30}}}}}$

Option a is correct.

$\textbf {\underline {\underline {Step-By-Step\:Explanation}}}$

$\sf{\underline{\blue {Given:}}}$

• Total students = 10
• Averaged marks obtained by them = 30
• Average marks obtained by first six students = 20
• Average marks obtained by last five is 42

$\sf {\underline{\blue{To\:Find:}}}$

• Marks obtained by the sixth student.

$\huge\underline\green {\tt Solution:}$

Average marks = mean

➡ Mean of 10 students

= $\dfrac {Sum\:of\:marks\:obtained\:by\:10\:students}{Total\:students}$

$30 = \dfrac {sum\:of\:marks\:obtained\:by\:10\:students}{10}$

➡ 300 = Sum of marks obtained by 10 students

Now,

➡ Mean of first 6 students

$20= \dfrac {sum\:of\:marks\:obtained\:by\:10\:students}{6}$

➡ 120 = sum of marks obtained by 6 students -- ( i )

Again,

➡ Mean of last five students

$42 = \dfrac {sum\:of\:marks\:obtained\:by\:last\:5\:students}{5}$

➡ 210 = sum of marks obtained by last five students. -------- ( ii )

Finally,

Add ( i ) and ( ii )

We get,

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

➡ 330 = ( L + M + N + O + P + Q ) + ( Q + R + S + T + U )

● Sum of marks of 10 students = 300

So,

330 = 300 + Q

➡ Q = 330 - 300

•°• Q = 30

Therefore,

Marks obtained by the sixth student is 30

Answer 2

Answer: 30

Step-by-step explanation:

Given that there are 10 students in the class.

Let the marks of those students be  x₁ , x₂ , x₃ , x₄ , x₅ , x₆ , x₇ , x₈ , x₉ , x₁₀ respectively.

Given that average of these numbers of 10 students is 30.

We know that,

$\text{Average}=\frac{\text{Sum of total marks}}{\text{Number of Students}}\\\;\\30=\frac{x_1+x_2+..............+x_{10}}{10}\\\;\\300=x_1+x_2+x_3+x_4+x_5+x_6+x_7+x_8+x_9+x_{10}\;\;\;\;...........(i)$

Again its given that average of first six students is 20

$20=\frac{x_1+x_2+x_3+x_4+x_5+x_6}{6}\\\;\\120=x_1+x_2+x_3+x_4+x_5+x_6\\\;\\x_1+x_2+x_3+x_4+x_5+x_6=120\;\;\;\;...........(ii)$

Now, average of last five students is 42,

$42=\frac{x_6+x_7+x_8+x_9+x_{10}}{5}\\\;\\210=x_6+x_7+x_8+x_9+x_{10}\\\;\\x_6+x_7+x_8+x_9+x_{10}=210\;\;\;\;...........(iii)$

Adding equation ii) and iii)

$x_1+x_2+x_3+x_4+x_5+x_6+x_6+x_7+x_8+x_9+x_{10}=120+210\\\;\\(x_1+x_2+x_3+x_4+x_5+x_6+x_7+x_8+x_9+x_{10})+x_6=330\;\;\;\;\;\;\text{[From equation i)]}\\\;\\300+x_6=330\\\;\\x_6=330-300\\\;\\x_6=30$

Hence marks obtained by sixth student is 30