Question

The numerator of a fraction is 4 less than the denominator. If 1 is added to
both its numerator and denominator, it becomes 13. Find the fraction.

Answer 1

check the attachment... the solution is in it

Answer 2

Answer:

The fraction $\dfrac{x}{y}$ is $\dfrac{4}{1}$    .

Step-by-step explanation:

Given as :

Let The fraction = $\dfrac{numerator}{denominator}$ =  $\dfrac{x}{y}$

The numerator of a fraction is 4 less than the denominator.

i.e numerator = denominator - 4

Or, x = y - 4              ........A

Again

If 1 is added to  both its numerator and denominator, it becomes 13.

i.e  $\dfrac{x + 1}{y + 1}$ = 13

Or, x + 1 = 13 × ( y + 1 )

Or, x + 1 = 13 y + 13

or, x - 13 y = 13 - 1

Or, x - 13 y = 12           ..........B

Solving A and B

∵  x - 13 y = 12

Or, (y - 4) - 13 y = 12

or, y - 4 - 13 y = 12

Or, - 12 y = 12 + 4

Or, - 12 y = 16

∴      y = $\dfrac{16}{-12}$

i.e  y = $\dfrac{-4}{3}$

Put the value of y in eq A

x =  $\dfrac{-4}{3}$- 4      

Or, x = $\dfrac{-4-12}{3}$

∴   x = $\dfrac{-16}{3}$

So, The fraction $\dfrac{x}{y}$ = $\dfrac{\dfrac{-16}{3} }{\dfrac{-4}{3} }$

Hence , The fraction $\dfrac{x}{y}$ is 4  . Answer