Question

A fraction becomes 1/3 when 1 is subtracted from the numerator it becomes 1/4 when 8 is added to the denominator . Find the fraction

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Answer 1

$\huge\bold{\textbf{\textsf{{\color{cyan}{Answer}}}}}$

Given :-

A fraction becomes 1/3 when 1 is subtracted from the numerator.

It become 1/4 when 8 is added to its denominator.

Solution :-

Let the fraction be x/y

According to the question,

⇒ x-1/y = 1/3

⇒ 3x - y = 3... (i)

⇒ x/y + 8 = 1/4

⇒ 4x - y = 8 ... (ii)

Subtracting equation (i) from equation (ii), we

get

⇒ x = 5 ... (iii)

Putting this value in equation (i), we get

⇒15 - y = 3

⇒ y = 12

Hence, the fraction is 5/12.

Answer 2

$\huge \bold\color{lime}\maltese \color{orange}A \color{red}n \color{green}s \color{blue}w \color {purple}e \color {lavender}r$

Let the numerator be x and the denominator be y

then the fraction is $\large\frac{x}{y}$

When 1 is subtracted from the numerator we get $\large \frac{1}{3}$

i.e., $\large\frac{x - 1}{y} = \frac{1}{3}$

while cross multiple we get,

3x - 3 = y

3x - y = 3_______(i)

When 8 is added to the denominator we get $\large\frac{1}{4}$

i.e., $\large\frac{x}{y + 8} = \frac{1}{4}$

while cross multiple we get,

4x = y + 8

4x - y = 8_______(ii)

Now subtracting (i) and (ii) we get,

-x = -5

then, x = 5

Apply x = 5 in (i)

3(5) - y = 3

15 - y = 3

-y = 3 - 15 = -12

then, y = 12

∴ Numerator = x = 5

Denominator = y = 12

$\implies the \: fraction \: is \: \frac{5}{12}$