In gurukul 60% of students ae boys , p% of boys and q% of girl are passed the total number of pass boys and fail girl are equal to total number of pass girl and fail boys . Find value of p and q if both are integers
Answers
Given : In gurukul, 60% of students are B , p% of B and q% of G are pa ss . The total number of pa ss B and fail G are equal to total number of pa ss G and fail B
To Find : value of p and q if both are integers.
Solution:
Let say number of students in gurukul = 1000S
60% of students are B =>B = (60/100)1000S = 600S
G = 1000S - 600S = 400S
p% of B and q% of G are pa ss
=> (p/100) 600S = 6pS B pa ss
failed B = 600S - 6pS
(q/100) 400S = 4qS G pa ss
failed G = 400S - 4qS
The total number of pa ss B and fail G are equal to total number of pa ss G and fail B
6pS + 400S - 4qS = 4qS + 600S - 6pS
=> 12pS = 8qS + 200S
=> 12p - 8q = 200
=> 3p - 2q = 50
q = 2 then p = 18
q = 5 then p = 20
q = 8 then p = 22
q = 11 then p = 24
q = 14 then p = 26
q = 17 then p = 28
and so on
q = 50 , p = 50
q = 53 p = 52
q = 95 p = 80
q = 98 p = 82
Hence 33 possible pair of values
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