Question

The sum of the numerator and the denominator is 16. If 5 is added to its denominator then its value is 1/2 then it is a fraction ----.please give to answer right amd fast . its option a(a) 9/7 b.4/12 c.7/9 d.12/4.​

Answer 1

Given :

• The sum of the numerator and the denominator is 16 .
• If 5 is added to its denominator then it's value is 1/2.

To find :

• Original fraction .

Solution :

Consider,

• Numerator = x
• Denominator = y

According to the 1st condition :-

• The sum of the numerator and the denominator is 16 .

$\implies\sf{x+y=16}$

$\implies\sf{x=16-y...........(1)}$

According to the 2nd condition :-

• If 5 is added to its denominator then it's value is 1/2.

$\implies\sf{\dfrac{x}{y+5}=\dfrac{1}{2}}$

$\implies\sf{\dfrac{16-y}{y+5}=\dfrac{1}{2}\:[put\:x=16-y\: from\:eq(1)]}$

$\implies\sf{32-2y=y+5}$

$\implies\sf{-2y-y=5-32}$

$\implies\sf{-3y=-27}$

$\implies\sf{y=9}$

• Denominator = 9

Now , put y = 9 in eq(1) for getting the value of x.

$\implies\sf{x=16-y}$

$\implies\sf{x=16-9}$

$\implies\sf{x=7}$

• Numerator = 7

Therefore,

${\boxed{\bold{Original\: fraction=\dfrac{7}{9}}}}$

Option (C) is correct.

Answer 2

Let

• Numerator = x , Denominator = y

case 1st

→ the sum of numerator and denominator = 16

$\rightarrow x+y=16 \\ \rightarrow x-16=-y-----equ(1)$

Case 2nd

→ if 5 is added to its denominator then it will be 1/2

$\rightarrow\tt x\frac{y+5}=\frac{1}{2}\\ \rightarrow\tt \frac{16-y}{y+5}=\frac{1}{2}\\ \rightarrow\tt 32-2y= y+5 \\ \rightarrow\tt -2-y=5-32 \\ \rightarrow\tt-3y=27\\ \rightarrow\tt y=\frac{27}{3}\\ \rightarrow\tt y=9$

$\rule{230}2$

put y=9 in eq(1)

x-9=-16

x=9-16

x=7

Hence,

The original fraction is $\large\frac{1}{7}$