Question

the denominator of the fraction is 4 more than twice the numerator when both numerator and denominator are decrease by 6 then the denominator become 12 times the numerator determine
the fraction

Answer 1

$hi....$
Let the numerator be x and the denominator be y.

By the given condition ,

y = 2x + 4

2x - y = -4 ...........................(1)

By the second given condition ,

y - 6 = 12(x - 6)

y - 6 = 12x - 72

-6 + 72 = 12x - y

66 = 12x - y

12x - y = 66 .........................(2)

[Subtracting equation no. (2) from (1)]

2x - y = -4
12x - y = 66
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-10x = -70
10x = 70
x = 70 / 10
x = 7

Substitute x = 7 in equation no. (1)

2x - y = -4
2(7) - y = -4
14 - y = -4
14 + 4 = y
y = 18

So .....
we get ,

$x = 7 \: \: \: . \: \: \: y = 18$
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Final Answer :
$fraction = \frac{x}{y} = \frac{7}{18}$
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$hope \: \: this \: \: helps....$