Question

The denominator of a fraction is 2 more than its numerator. If the numerator is decreased
by 1 and denominator is increased by 2 , the new fraction becomes equivalent to 2
7
. What
is the original fraction

Answer 1

Answer:

ans = 3/5

Step-by-step explanation:

Let the numerator be x

Then the denominator will be x+2

ATQ

=>x+1/x+2+1=2/3

=>x+1/x+3=2/3

=>3 (x+1)=2 (x+3)

=>3x+3=2x+6

=>3x-2x=6-3

=>x=3

The fraction is 3/5.

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Answer 2

Answer:

$\frac{5}{7}$

Step-by-Step Explanation:

Let the numerator be x

∴ The denominator is x + 2

$\frac{x}{x+2}$

After decreasing the numerator by 1 and denominator by 2, the new number will be:

$=>\frac{x-1}{x + 2+2} = \frac{2}{7}$

$=>\frac{x}{x+4} = \frac{2}{7}$

Translocating the denominators, we get:

$=> 7(x-1) = 2 (x+4)$

$=> 7x -7 = 2x +8$

$=> 7x - 2x = 8 + 7$

$=>5x = 15$

$=> x =5$

∴ The original fraction will be $\frac{x}{x+2} = \frac{5}{5+2} =\frac{5}{7}$