a fraction becomes 1 by 3 when 2 is subtracted from numerator and become 1 by 2 when 1 is subtracted from denominator. find fraction
Answers
Let the numerator be X and denominator be y
According to question,
X-2/y=1/3
3X-6=y...(1)
X/y-1=1/2
2X=y-1.....(2)
Substitute eq.(1) in eq.(2)
2X=3X-6-1
2X-3X=-7
-X=-7
X=7
Substitute this value in eq.(2)
2X=y-1
2(7)=y-1
14+1=y
y=15
So fraction become 7/15
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Given:
On subtracting two from the numerator of a fraction, the resulting fraction is 1/3.
On subtracting one from the denominator in a fraction, the resulting fraction is 1/2.
To find:
To calculate the fraction.
Solution:
Let us assume the fraction as X/Y.
Let X be the numerator.
Let Y be the denominator.
After subtracting two from the numerator,
The fraction becomes,
(X-2 )/Y = 1/3 (equation 1)
On cross multiplication,
3X – 6 = Y
3X – Y = 6 (equation 2)
After subtracting one from the denominator,
The fraction becomes,
X/(Y-1) =1/2 (equation 3)
On cross multiplication,
2X = Y – 1
2X – Y = -1 (equation 4)
Solving equations 2 and 4, we get,
The numerator of the fraction, X= 7
Putting X = 7, in equation 2,
Denominator of fraction, Y = 15
The fraction was X/Y.
After putting the values of X and Y,
The fraction is = 7/15