Question

numerator of fraction is three less than its denominator if numerator is increased by 1 and denominator is increased by 3 . the fraction become 1/2 find original number.​

Answer 1

According to the question the numerator is 3 less than its denominator

The fraction will be -

$\frac{x - 3}{3}$

Now if if numerator is increased by 1 and denominator is increased by 3 the fraction become 1/2.

From this condition we will form this linear equation,

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

We shall simply solve this equation to get the answer ,

$\frac{x - 3 + 1}{x + 3} = \frac{1}{2} \\ \\ \\ \implies \frac{x - 2}{x + 3} = \frac{1}{2} \\ \\ \\ \implies 2(x - 2) = x + 3 \\ \\ \\ \implies 2x - 4 = x + 3 \\ \\ \\ \\ \implies \boxed{ \boxed{x = 7}}$

Now if x = 7 the fraction will be,

x - 3 / x = 4/7 [ANS]

VERIFICATION :-

LHS =

$\frac{4}{7} \\ \\ = \frac{4 - 1}{7 + 3} \\ \\ \\ = \frac{5}{10} \\ \\ \\ = \frac{1}{2}$

= RHS

Hence , LHS = RHS , Our answer is correct.