Question

a fraction becomes 1/3 when 1 is added to the denominator if 1 is added to the nuumerator the fraction becomes 1/2 find the fraction

Answer 1

Answer:

→ $\sf The \: fraction\:is\: \dfrac{3}{8}$

Given:

• If 1 is added to the denominator, the fraction becomes 1/3
• if 1 is added to the numerator, the fraction becomes 1/2

To Find:

• The Fraction.

Solution:

Let the numerator is x, and the denominator is y.

so the fraction is x/y

It is given that:

⇛ $\sf \dfrac{x+1}{y}=\dfrac{1}{2}$

⇛ $\sf y = 2(x+1) = 2x+2$

now, we've got the value of y that is interdependent on x.

It is also given that-

⇛ $\sf \dfrac{x}{y+1}=\dfrac{1}{3}$

By using (1), we could substitute (2x + 2) instead of y

⇛⠀$\sf \dfrac{x}{(2x+2)+1}=\dfrac{1}{3}$

⇛⠀$\sf 3(x)=2x+2+1$

⇛⠀$\sf 3x=2x+3$

⇛⠀$\sf 3x-2x =3$

⇛⠀$\sf x =3$

we got x = 3

then y = 2x + 2 = 2(3) + 2 = 8

⠀⠀

⠀⠀⠀⠀$\sf \boxed{\bold{The \: Fraction\: is\: \dfrac{3}{8}}}$

⠀⠀

Verification:

1. If we add 1 to denominator, the fraction should become 1/3

➞ $\sf \dfrac{3}{8+1}=\dfrac{3}{9}=\dfrac{1}{3}$

2. If we add 1 to numerator, the fraction should become 1/2.

➞$\sf \dfrac{3+1}{8}=\dfrac{4}{8}=\dfrac{1}{2}$

satisfies both conditions!

Hence verified!⠀⠀⠀⠀⠀⠀⠀⠀⠀