Question

the numerator of a fraction is 6 less than its denominator if the numerator is decreased by 4 denominator is decreased by 1 the fraction becomes 5 /8 find the fraction​

Answer 1

SOLUTION :-

Let,

Numerator = x

Denominator = y

According to the first condition,

$\longrightarrow \sf x= y-6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(1)$

According to the second condition,

$\longrightarrow\sf \dfrac{x-4}{y-1}=\dfrac{5}{8} \\\\\longrightarrow 8(x-4)=5(y-1) \\\\\longrightarrow 8x-32=5y-5 \\\\\longrightarrow 8x-5y= 27 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(2)$

Substitute the value of x in equation (2),

$\longrightarrow \sf 8(y-6)-5y= 27 \\\\\longrightarrow 8y-48-5y = 27 \\\\\longrightarrow 8y-5y= 27+48\\\\\longrightarrow 3y = 75 \\\\\longrightarrow\bf y = 25$

Denominator = 25

Numerator = 25 - 6 = 19

$\bf FRACTION = \dfrac{19}{25}$