In Sivakasi, each boy’s quota of match sticks to fill into boxes is not more than 200 per session. If he reduces the number of sticks per box by 25, he can fill 3 more boxes with the total number of sticks assigned to him. Which of the following is the possible number of sticks assigned to each boy?
Answers
Given : each boy’s quota of match sticks to fill into boxes is not more than 200 per session. If he reduces the number of sticks per box by 25, he can fill 3 more boxes with the total number of sticks assigned to him
To find :
Solution:
Number of Sticks assigned S ≤ 200
Number of Boxes = B
Sticks in Each Box = S/B
he reduces the number of sticks per box by 25, he can fill 3 more boxes with the total number of sticks assigned to him
=> (S/B - 25) * ( B + 3) = S
=> (S - 25B)(B + 3) = BS
=> BS + 3S - 25B² - 75B = BS
=> 25B² + 75B = 3S
S ≤ 200
=> 25B² + 75B ≤ 3(200)
=> B² + 3B ≤ 3(8)
=> B² + 3B ≤ 24
=> (B + 3/2)² - 9/4 ≤ 24
=> (B + 3/2)² ≤ 85/4
B + 3/2 ≤ 9/2
=> B ≤ 3
B = 1 , 2 , 3
25B² + 75B = 3S
B = 1 => 3S = 100 => S = 100/3 not possible
B = 2 => 3S = 250 => S = 250/3 not possible
B = 3 => 3S = 450 => S = 450/3 = 150
150 is possible number of Stick assigned
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