Question

The denominator of a fraction is 4 more than its numerator. If 2 is added to the numerator and 5 is subtracted from the denominator, the fraction becomes 5/2. Find the fraction.​

Answer 1

Answer:

$\frac{3}{7}$

Step-by-step explanation:

Let the numerator be x.

denominator= x+4 (as it is 4 more than the numerator (x))

the original fraction = $\frac{x}{x+4}$

If 2 is added to the numerator and 5 is subtracted from the denominator, then

numerator = x+2

denominator = (x+4)-5

                     = x-1

The new fraction =  $\frac{x+2}{x-1}$ = $\frac{5}{2}$

After cross multiplication:

2(x+2) = 5(x-1)

= > 2x +4 = 5x -5

=> 5x - 2x = 4+5

=> 3x = 9

=> x = 3

∴ The original fraction = $\frac{x}{x+4}$

                                     $= \frac{3}{3+4} \\= \frac{3}{7}$