lf you added to a the denominator of a fraction and the fraction is simplified we get 1/4 if instead 1 is added to the numerator and simplified we GET 2/5 what is the fraction
Answers
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Given :- lf you added 2 to the denominator of a fraction and the fraction is simplified we get 1/4. if instead 1 is added to the numerator and simplified we get 2/5. what is the fraction ?
Solution :-
Let us assume that, the fraction is x/y .
Case 1):- when 2 is added to the denominator .
→ x/(y + 2) = 1/4
→ 4x = y + 2
→ 4x - y = 2 --------- Eqn.(1)
Case 2):- when 1 is added to the numerator.
→ (x + 1)/y = 2/5
→ 5x + 5 = 2y
→ 5x - 2y = (-5) --------- Eqn.(2)
Multiply Eqn.(1) by 2 and than subtracting from Eqn.(2),
→ (5x - 2y) - 2(4x - y) = (-5) - 2(2)
→ 5x - 8x - 2y + 2y = (-5) - 4
→ (-3x) = (-9)
→ x = 3
Putting value of x in Eqn.(1),
→ 4*3 - y = 2
→ y = 12 - 2
→ y = 10 .
Therefore,
→ Required fraction = x/y = (3/10) . (Ans.)
Hence the fraction is (3/10).
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