When one is added to the numerator as well as the denominator of a certain fraction, if becomes 1/2 and if one is subtracted from the numerator and denominator both, the fraction becomes 1/3 . Find the original fraction.
Answers
Answer:
Let us assume, x be the numerator and y be the denominator of a fraction.
Therefore, given fraction is x/y
Given:
(x-1) / (y-1) = 1/3
3x - 3 = y - 1
3x - y = 2
y = 3x - 2 -------------------1
Also given:
(x+1) / (y+1) = 1/2
2x + 2 = y + 1
y - 2x = 1 -------------2
Substitute the value of y from equation 1
3x - 2 - 2x = 1
x - 2 = 1
x = 1 + 2
x = 3
Therefore, y = 3x - 2 = 3 * 3 - 2 = 7
y = 7
Therefore, the given fraction: 3/7
Answer :
The original fraction is 2/5.
what is fraction?
A fraction is a numerical quantity that represents a part of a whole or a ratio between two numbers, indicated by a numerator and a denominator separated by a horizontal line.
Explanation :
Let's assume the original fraction to be x/y.
According to the problem statement:
(x+1)/(y+1) = 1/2 ---- (1)
(x-1)/(y-1) = 1/3 ---- (2)
From equation (1), we can rewrite it as x+1 = (y+1)/2, which gives us:
x = (y/2) - (1/2)
Substituting this value of x in equation (2), we get:
((y/2) - (3/2))/(y-2) = 1/3
Simplifying this equation, we get:
3y - 9 = 2y - 4
Solving for y, we get:
y = 5
Substituting the value of y in equation (1), we get:
x = 2
Therefore, the original fraction is 2/5.
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