Question

The numerator of the fraction is 4 less than the denominator.if the numerator is decreased by 2 and denominator is increased by 1,then the denominator becomes 8 times the numerator.find the fraction?

Answer 1

$\bold{\underline{\underline{\purple{Given :}}}}$

• The numerator of a fraction is 4 less than the denominator .
• If numerator is decreased by 2 and denominator is increased by 1 then the denominator becomes 8 times of numerator .

$\bold{\underline{\underline{\purple{To \ Find :}}}}$

• The Fraction

$\bold{\underline{\underline{\purple{Solution :}}}}$

Suppose the numerator be x

And , Suppose the denominator be y

According to First Case :

$\implies \bold{\sf{x = y - 4}}$.....1) Equation

According to Second Case :

$\implies \bold{8(x - 2) = y + 1}$

$\implies \bold{8x - 16 = y + 1}$

$\implies \bold{8x - y = 17}$

$\implies \bold{\sf{8 ( y - 4) - y = 17}}$

$\big(\big} \sf{From the first Equation value of x put} \big)\big}$

$\implies \bold{\sf{8y - 32 - y = 17}}$

$\implies \bold{\sf{7y = 17 + 32}}$

$\implies \bold{\sf{7y = 49}}$

$\implies \bold{\sf{ y = \frac{49}{7}}}$

$\implies \boxed{\bold{ y = 7}}$

Put the value of y in equation 1) :-

$\implies \bold{ x = y - 4}$

$\implies \bold{ x = 7 - 4}$

$\implies \boxed{\bold{ x = 3}}$

The fraction = $\bold{\frac{3}{7}}$

$\rule{200}2$

Answer 2

Step-by-step explanation:

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