The numerator of a fraction is 4 less than the denominator. If the numerator is decreased by 2 and the denominator is increased by 1, then the denominator is eight times the numerator. Find the fraction.

Shahariar Rijon

February 21, 2022

0

Solution

Let fraction be $\frac{x}{y}$
According to question
$x = y - 4$
$\Rightarrow x - y + 4 = 0$ .......(i)
and $8 (x - 2) = y + 1$
or $8 x - 16 = y + 1$
or $8 x - y - 17 = 0$ ........(ii)
Solving (i) and (ii), we get (refer to image)
$\Rightarrow \frac{x}{1 7 + 4} = \frac{y}{3 2 + 1 7} = \frac{1}{- 1 + 8}$
$\Rightarrow \frac{x}{2 1} = \frac{y}{4 9} = \frac{1}{7}$
$\Rightarrow x = \frac{2 1}{7} = 3 \Rightarrow y = \frac{4 9}{7} = 7$
Hence, required fraction is $\frac{3}{7} .$

Tags

Linear Equations Maths

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The numerator of a fraction is 4 less than the denominator. If the numerator is decreased by 2 and the denominator is increased by 1, then the denominator is eight times the numerator. Find the fraction.

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