A fraction becomes 2/5 when 2 is subtracted from the numerator and denominator it becomes 3/4 when 5 is added to its denominator and numerator, find the fraction.
Answers
Let the numerator be x and the denominator be y.
Therefore, the original fraction be x/y.
Given that when 2 is subtracted from the numerator and denominator, it becomes (2/5).
= > (x - 2)/(y - 2) = (2/5)
= > 5(x - 2) = 2(y - 2)
= > 5x - 10 = 2y - 4
= > 5x - 2y = 6 ------ (1)
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Given that when 5 is added to its denominator and numerator, it becomes 3/4.
= > (x + 5)/(y + 5) = (3/4)
= > 4(x + 5) = 3(y + 5)
= > 4x + 20 = 3y + 15
= > 4x - 3y = -5 ------ (2)
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On solving (1) * 4 & (2) 5, we get
= > 20x - 8y = 24
= > 20x - 15y = -25
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7y = 49
y = 7.
Substitute y = 7 in (1), we get
= > 5x - 2y = 6
= > 5x - 2(7) = 6
= > 5x - 14 = 6
= > 5x = 20
= > x = 4.
Therefore, the original fraction = (4/7).
Hope this helps!
Step-by-step explanation:
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