Question

when 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes 1/4 when 6 is added to numerator and denominator is multiplied by 3 it becomes 2/3 find the fraction.
can anyone please send me the solution of this problem

Answer 1

Solve these equations simultaneously and get the answers by substitution. fraction is y/x which is equal to 4/5

Answer 2

Answer:

$Original \: fraction=\frac{x}{y}\\=\frac{4}{5}$

Step-by-step explanation:

Let numerator = x ,

Denominator = y,

according to the problem given,

i) when 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes 1/4

$\frac{x-2}{y+3}=\frac{1}{4}$

$\implies 4(x-2)=y+3$

$\implies 4x-8=y+3$

$\implies 4x-8-3=y$

$\implies 4x-11=y---(1)$

ii)when 6 is added to numerator and denominator is multiplied by 3 it becomes 2/3

$\frac{x+6}{3y}=\frac{2}{3}$

$\implies \frac{3(x+6)}{3}=2y$

$\implies x+6=2y$

$\implies x+6 = 2(4x-11)\:[From \:(1)]$

$\implies x+6 = 8x-22$

$\implies 6+22=8x-x$

$\implies 28=7x$

$\implies \frac{28}{7}=x$

$\implies 4=x$

$Put \: x = 4 \: equation \:(1)\\we\:get ,\\y=4\times 4-11$

$\implies y = 16-11$

$\implies y = 5$

$Original \: fraction=\frac{x}{y}\\=\frac{4}{5}$

Therefore,.

$Original \: fraction=\frac{x}{y}\\=\frac{4}{5}$

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