Question

A fraction becomes 6/5 , if 1 is added to each of numerator and denominator . However if we subtract 5 from each the fraction becomes 3/2 . Find the fraction

Answer 1

the fraction is 11/9

Answer 2

The fraction is $\frac{11}{9}$.

Step-by-step explanation:

Given:

A fraction becomes $\frac{6}{5}$, if 1 is added to each of numerator and denominator . However if we subtract 5 from each the fraction becomes $\frac{3}{2}$.  

To find:

Find the fraction

Solution:

$\frac{(x + 1)}{(y + 1)} = \frac{6}{5}$

Simplifying,

we get x = $\frac{(6y + 1)}{5}$ … (1)

Also given,

$\frac{(x - 5)}{(y - 5)} = \frac{3}{2}$

Simplifying we get 2x – 3y = -5 …(2)

Substitute (1) in (2)

$2 [\frac{(6y + 1)}{5}] - 3y = -5$

-3y = -27

y = 9,  

x = 6(9) + $\frac{1}{5}$= 11

The fraction is $\frac{11}{9}$.

To Know More:

A fraction becomes 4/5 if 1 is added to both numerator and denominator.  If however, 5 is subtracted from both numerator and denominator, the fraction becomes 1/2. Find the fraction.

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