Question

the sum of numerator and denominator is 14.if 2 is added to the numerator and 2 is subtracted the denominator it becomes 5÷3.​

Answer 1

Step-by-step explanation:

Let the numerator and denominator be x and y x+2÷y-2 =5÷3

Answer 2

The required fraction =$\dfrac{\dfrac{27}{4}}{\dfrac{29}{4}} =\dfrac{27}{29}$

Step-by-step explanation:

Let the required fraction be $\dfrac{x}{y}$.

To find, the required fraction = ?

According to question,

x + y = 14               .............(1)

and

$\dfrac{x+2}{y-2} =\dfrac{5}{3}$

By crossmultiplication,

3(x + 2) = 5(y -2)

⇒ 3x + 6 = 5y - 10

⇒ 3x - 5y = - 16           .........(2)

Multiplying equation (1) by 5 and adding (2), we get

5x + 5y + 3x - 5y = 70 - 16

⇒ 8x = 54

⇒ $x=\dfrac{27}{4}$

Put $x=\dfrac{27}{4}$ in equation (1), we get

$\dfrac{27}{4}$ + y = 14      

⇒ y = 14 - $\dfrac{27}{4}$

⇒ y = $\dfrac{29}{4}$

∴  The required fraction =$\dfrac{\dfrac{27}{4}}{\dfrac{29}{4}} =\dfrac{27}{29}$