Question

9. The numerator of a fraction is 5 less than the denominator. If 1 is added to both the numerator and the denominator the fraction would become 2/3. Find the original fraction

Answer 1

Answer:

14/19

Step-by-step explanation:

Let the fraction be x-5/x

x-5+1/x+1  =  2/3

x-4/x+1==2/3

Cross multiplication:

3(x-4)=2(x+1)

3x-12=2x+2

x=14

The original fraction is :  14/19

Answer 2

Question:

The numerator of a fraction is 5 less than the denominator. If 1 is added to both the numerator and the denominator ,the fraction would become 2/3 . find the original fraction.

Answer:

$\frac{9}{14}$

Solution:

let,

numerator of fraction = x

then,

according to the question

denominator of fraction will be = x + 5

so the fraction will be,

$\frac{x}{x + 5}$

on adding 1 on both numerator and denominator of fraction it will become 2/3

hence,

$\frac{x + 1}{x + 5 + 1} = \frac{2}{3} \\ \\ \frac{x + 1}{x + 6} = \frac{2}{3} \\ \\ (cross \: multiplying) \\ \\ 3x + 3 = 2x + 12 \\ \\ 3x - 2x = 12 - 3 \\ \\ x = 9$

we get x as 9 hence the original fraction will be

$\frac{x}{x + 5} = \frac{9}{9 + 5} = \frac{9}{14} \\ \\ therefore \: the \: original \\ \: fraction \: is \: \frac{9}{14} .$

Verification of answer:

It is given that if in original fraction the numerator and denominator are increased by 5 then the fraction becomes 2/3

so,

adding 1 in both numerator and denominator

(9+1) /(14+1) = 10 / 15 = 2/3

the fraction became 2/3 on adding 1 in both numerator and denominator

hence ,

Verified.