The denominator of a fraction is 4 more than the numerator. If 1 is added to the numerator and 2 is added to the denominator, the value of the fraction becomes 4/5. Find the original fraction.
Answers
Let the numerator and denominator of the given fraction be x and y respectively.
According to the question,
Case 1 :-
Denominator of the fraction is 4 more than the numerator.
⇒ Numerator = Denominator - 4
⇒ x = y - 4 ...(1)
Case 2 :-
If 1 is added to the numerator and 2 is added to the denominator, the value of fraction becomes 4/5
⇒ (Numerator + 1) / (Denominator + 2) = 4/5
⇒ (x + 1) / (y + 2) = 4/5
⇒ 5(x + 1) = 4(y + 2)
⇒ 5x + 5 = 4y + 8
⇒ 5x - 4y = 3 ...(2)
Substituting the value of x from (1) in (2), we have
⇒ 5(y - 4) - 4y = 3
⇒ 5y - 20 - 4y = 3
⇒ y = 23
Similarly, Substitute y = 23 in (1),
⇒ x = 23 - 4
⇒ x = 19
Now, At the beginning of our solution we took the numerator & denominator to be x & y respectively. So the fraction is:
⇒ x / y
⇒ 19/23
Hence, The fraction is 19/23
Answer:
19/23
Step-by-step explanation:
Assume that the numerator is x and denominator is y.
The denominator of a fraction is 4 more than the numerator.
As per given condition,
→ y = x + 4 ............(1)
If 1 is added to the numerator and 2 is added to the denominator, the value of the fraction becomes 4/5.
As per given condition,
→ (x + 1)/(y + 2) = 4/5
→ 5(x + 1) = 4(y + 2)
→ 5x + 5 = 4y + 8
→ 5x + 5 = 4(x + 4) + 8 [From (1)]
→ 5x + 5 = 4x + 16 + 8
→ x = 19
Substitute value of x in (1)
→ y = 19 + 4
→ y = 23
Hence, the original fraction = x/y = 19/23.