Question 127

A fraction becomes $$\frac{4}{5}$$ if 1 is added to both its numerator and denominator while it becomes $$\frac{1}{2}$$ if 5 is subtracted from its numerator and denominator. The fraction is

Solution

$$\frac{x+1}{y+1}$$=$$\frac{4}{5}$---------equation 1

$$\frac{x-5}{y-5}$$=$$\frac{1}{2}$$---------equation 2

from equation 1 and 2,

5x-4y=-1------ multiply with 2

2x-y=5----------multiply with 5

therefore

10x-8y=-2-----(1)

10-5y=25------(2)

by subtracting we get Y=9

subsitute y value in any equation we get X=7

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