A fraction becomes 9/11, if 2 added to the both numerator and denominator, if 3, is added to both numerator and denominator it becomes 5/6 find the fraction?
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Answer:
Fraction = 7/9
Step-by-step explanation:
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Let the fraction be x/y, numerator = x, denominator = y
According to question
x+2/y+2 = 9/11
= 11 (x+2) = 9 (y+2)
= 11x + 22 = 9y + 18
= 11x - 9y = -4
Now,
x+3 / y+3 = 5/6
= 6 (x+3) = 5 (y+3)
= 6x + 18 = 5y + 15
= 6x - 5y = -3
Using elimination method
55x - 45y = -20
-- 54x - 45y = -27
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after solving this, we get x = 7
putting value of x in any of this equations, we get y = 9
Fraction = 7/9
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