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There are three groups G(1), G(2) and G(...

There are three groups `G_(1), G_(2) and G_(3)` in a College with 20, 40 and 60 students respectively. The average marks obtained by groups `G_(1), G_(2) and G_(3)` are 50%, 60% and 70% respectively. Find the average marks of the entire college?

A

`60%`

B

`63%`

C

`62%`

D

`61%`

Text Solution

AI Generated Solution

The correct Answer is:
To find the average marks of the entire college, we will follow these steps: ### Step 1: Calculate the total marks for each group. - For Group G1: - Number of students = 20 - Average marks = 50% - Total marks = Number of students × Average marks = 20 × 50 = 1000 - For Group G2: - Number of students = 40 - Average marks = 60% - Total marks = Number of students × Average marks = 40 × 60 = 2400 - For Group G3: - Number of students = 60 - Average marks = 70% - Total marks = Number of students × Average marks = 60 × 70 = 4200 ### Step 2: Sum the total marks of all groups. - Total marks = Total marks of G1 + Total marks of G2 + Total marks of G3 - Total marks = 1000 + 2400 + 4200 = 7600 ### Step 3: Calculate the total number of students. - Total number of students = Number of students in G1 + Number of students in G2 + Number of students in G3 - Total number of students = 20 + 40 + 60 = 120 ### Step 4: Calculate the average marks of the entire college. - Average marks = Total marks / Total number of students - Average marks = 7600 / 120 = 63.33% ### Final Answer: The average marks of the entire college is approximately **63.33%**.
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