A fraction is such that if the numerator is multiplied by3 and denominator is reduced by 3, we get 18/11, but if the numerator is increased by8 and denominator is doubled ,we get 2/5. Find the fraction
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Answer:
Step-by-step explanation:
Solution :-
Let the fraction be x/y.
Then,
According to the question
3x/y - 3 = 18/11
and x + 8/2y = 2/5
⇒ 11x = 6y - 18 and 5x + 40 = 4y
⇒ 11x - 6y + 18 = 0 and 5x - 4y + 40 = 0
By cross-multiplication. we get
⇒ x/(- 6) × 40 - (- 4) × 18 = - y/11 × 40 - 5 × 18 = 1/11 × (- 4) - 5 × (- 6)
⇒ x/- 240 + 72 = - y/440 - 90 = 1/- 44 + 30
⇒ x/- 168 = y/- 350 = 1/- 14
⇒ x = - 168/- 14 and y = - 350/- 14
⇒ x = 12 and y = 25
Hence, the fraction is 12/25
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