Respuesta :
Answer:
The fraction is [tex]\frac{4}{6}[/tex]
Option (B) is correct.
[tex]3n-2d=0[/tex] and [tex]4n+8=3d+6[/tex]
Step-by-step explanation:
Let n denotes numerator and d denotes denominator of the fraction.
Given : The ratio of the numerator to the denominator of a fraction is 2 to 3.
That is [tex]\frac{n}{d}=\frac{2}{3}[/tex]
Cross multiply , we get,
[tex]3n=2d[/tex]
Or, [tex]3n-2d=0[/tex] ........(1)
Also, given : . If both the numerator and the denominator are increased by 2, the fraction becomes 3/4
That is [tex]\frac{n+2}{d+2}=\frac{3}{4}[/tex]
Cross multiply , We get,
[tex]4{n+2}={3}{d+2}[/tex]
[tex]4n+8=3d+6[/tex] .........(2)
[tex]3d-4n=2[/tex] .......(3)
Thus, from (1) and (2) , option (B) follows.
Solving equation (1) and (3) to get the original fraction using elimination method,
3n - 2d = 0 ............(1)
and 3d - 4n = 2 .........(3)
Multiply equation (1) by 3 , we get ,
9n - 6d = 0 ..........(4)
Multiply equation (3) by 2 , we get ,
-8n + 6d = 4 ..........(5)
Adding (4) and (5) , we get,
9n - 6d -8n + 6d = 4 + 0
⇒ n = 4
Put n = 4 in (1), we get
3n - 2d = 0 ⇒ 3(4) - 2d = 0 ⇒ 12 -2d = 0 ⇒ 12 = 2d ⇒ d = 6
so, the numerator is 4 and the denominator is 6.
Thus, the fraction is [tex]\frac{4}{6}[/tex]
