Question

In a class of 60 students there are 20 girls who scored an average of 40 marks in the test, what is the average marks of the boys if the class average is 60 marks?

A) 60 B) 70 C) 50 D)

Answer 1

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⏺ Required Answer:

✏GiveN:

• There are 60 students.
• Out of them, 20 are girls.
• Average score of girls is 40.
• Average score of entire class = 60

✏To FinD:

• Find average score of boys.

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⏺ How to solve?

Just we need to visualise the question logically to get the answer. The concept we need to know is the average. Average is found by:

$\large{ \boxed{ \rm{Average = \dfrac{Total \: sum \: of \: all \: items}{Total \: no. \: of \: items} }}}$

By using this formula only, we can solve the question!!

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⏺ Solution:

Given, Total no. of students = 60

• Number of girls = 20
• Then, Number of boys = 60 - 20 = 40

According to formula,

$\large{ \rm{Average \: score = \dfrac{Total \: score \: all \: students}{No. \: of \: students}}}$

Total score = Total score of girls + Total score of boys.

We have, Total no. of students = 60

• Average of entire class = 60

By using formula,

$\large{ \rm{ \rightarrow \: Average \: score = \dfrac{Total \: score \: of \: all \: students}{No. \: of \: students} }} \\ \\ \large{ \rm{ \rightarrow \: 60 = \dfrac{Total \: score}{60} }} \\ \\ \large{ \rm{ \rightarrow \: total \: score = 60 \times 60}} \\ \\ \large{ \rm{ \rightarrow \: total \: score = 3600}}$

Given, Total number of girls = 20

• Average score of girls = 40

By using formula,

$\large{ \rm{ \rightarrow{Average \: score \: of \: girls = \dfrac{Total \: score}{No. \: of \: girls} }}} \\ \\ \large{ \rm{ \rightarrow{40= \dfrac{Total \: score \: of \: all \: girls}{20} }}} \\ \\ \large{ \rm{ \rightarrow \: total \: score \: of \: girls = 40 \times 20 }} \\ \\ \large{ \rm{ \rightarrow \: total \: score \: of \: girls = 800}}$

Also given, Total number of boys = 40

• Let their average be x

By using formula,

$\large{ \rm{ \rightarrow \: Average \: of \: boys = \dfrac{Total \: score \: of \: boys}{No. \: of \: boys} }} \\ \\ \large{ \rm{ \rightarrow \: x = \dfrac{Total \: score \: of \: boys}{40} }} \\ \\ \large{ \rm{ \rightarrow \: Total \: score \: of \: boys = 40x}}$

Already we know,

Total score of all students = Total score of boys + Total score of girls. So,

$\large{ \rm{ \rightarrow \: 3600 = 800 + 40x}} \\ \\ \large{ \rm{ \rightarrow \: 40x = 3600 - 800}} \\ \\ \large{ \rm{ \rightarrow \: 40x = 2800}} \\ \\ \large{ \rm{ \rightarrow \: x = \cancel{ \frac{2800}{40} }}} \\ \\ \large{ \rm{ \rightarrow \: x = \boxed{ \red{70}}}}$

Average of all boys = 70

✏ Option B

$\large{ \therefore{ \underline{ \underline{ \blue{ \rm{Hence \: solved \: \dag}}}}}}$

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