Question

The sum of numerator and denominator of a fraction is 17.if the denominator is decreased by 2,the fraction become 1/2.then the fraction is?

Answer 1

Answer:

5/12

Step-by-step explanation:

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Let the fraction be a/b

Given,

a + b = 17 ...................1

Also,

a/b-2 = 1/2.................2

From 1 ,

b = 17 - a ....................3

From 2,

Cross multiply you get,,,

(1)(b-2) = 2(a)

2a +2 = b

From 3,

2a + 2 = 17 - a

a = 5

b = 17-5 = 12

So the fraction is 5/12

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Answer 2

Given :

• The sum of numerator and denominator of a fraction is 17 .
• If the denominator is decreased by 2 , the fraction becomes 1/2.

To find :

• The fraction .

Solution :

Consider,

• Numerator = x
• Denominator = y

According to the 1st condition :-

• The sum of numerator and denominator of a fraction is 17.

$\to\sf{x+y=17}$

$\to\sf{x=17-y..............(I)}$

According to the 2nd condition :-

• If the denominator is decreased by 2, the fraction becomes 1/2.

$\to\sf{\dfrac{x}{y-2}=\dfrac{1}{2}}$

• Put x = 17-y from eq (I).

$\to\sf{\dfrac{17-y}{y-2}=\dftac{1}{2}}$

$\to\sf{34-2y=y-2}$

$\to\sf{-2y-y=-2-34}$

$\to\sf{-3y=-36}$

$\to\sf{y=12}$

• Denominator = 12

Now put y = 12 in eq(1).

$\to\sf{x=17-y}$

$\to\sf{x=17-12}$

$\to\sf{x=5}$

• Numerator = 5

Therefore ,

${\boxed{\sf{The\: fraction=\dfrac{5}{12}}}}$