6. The average age of 25 boys in a class
decreases by 6 months when a new boy
takes the place of a 20 yr old boy. Find the
age of new boy.
(1) 7 yr
(2) 7.5 yr
(3) 8 yr
(4) 8.5 yr
Answers
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Answer:
Let x be the age of the 25 boys.
Let y be the age of the new boy.
According to the question:
Total Age of the boys should be: 25x + y - 20
Therefore, Average age of the boys = (25x + y - 20)/25
Age decreases by 6 months = 6months / 1 year
=> 6 months / 12 months
=> 1/2
=> 0.5
x - [(25x + y - 20) / 25] = 0.5
=> 25x/25 - [(25x + y - 20) / 25] = 0.5 [ since 25x/25 = x ]
=> (25x - 25x - y + 20) = 0.5 x 25
=> -y + 20 = 12.5
=> y = 20 - 12.5
=> y = 7.5
The Age of new boy is 7.5 yrs old.
Step-by-step explanation:
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