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Option 5 : 17.8

Given:

Total number of boys and girls in the class = 50

The average age of all the boys = 20 years

The average age of all the girls = 15 years

Total number of boys = Total number of girls + 6

Formula Used:

Average age of a group of people  = Sum of age of all the people in the group/Total number of people in the group

Calculation:

Let the total number of girls in the class be x

So, the total number of boys in the class is (x + 6)

Hence, we get: 

x + (x + 6) = 50

⇒ x = 22

So, the total number of girls in the class = 22, and 

The total number of boys in the class = 22 + 6 = 28

So, we obtain the total age of all the boys and girls in the class = (28 × 20) + (22 × 15) = 890

The average age of all the 50 students in the class = 890/50 = 17.8 years

∴ The average age of the whole class is 17.8 years

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