if the numerator of a fraction is multiplied by 2 and its denominator is increased by a by 1 it becomes 1 however if the numerator is increased by 4 and the denominator is x to the function becomes half find the fraction
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if the numerator of a fraction is multiplied by 2 and its denominator is increased by a by 1 it becomes 1 however if the numerator is increased by 4 and the denominator is x to the function becomes half find the fraction
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Answer:
Step-by-step explanation:
Let the numerator be x
and the denominator be y
Therefore, fraction= x/y
Acc. to Ques.
(x * 2) / (y-5) = 6/5
=> 5 (x * 2) = 6 (y-5)
=> 5 (2x) = 6y - 30
=> 10x = 6y - 30
=> 10x - 6y = -30
on dividing the equation by 2
=> 5x - 3y= -15 ---(1)
And, (x + 8) / 2y = 2/5
=> 5 (x + 8) = 2 * 2y
=> 5x + 40= 4y
=> 5x - 4y = -40 ---(2)
now, On subtracting eq. (1) from (2), we get,
-y=-25
=> y = 25 ---(3)
Put eq. (3) in (1)
5x - 3y = -15
=>5x - 3 * 25 = -15
=>5x - 75 = -15
=>5x = -15 + 75
=>5x = 60
=>x = 60/5
=>x = 12
So, the fraction is 12/25