Question

Please help me with this sum . I HAVE GOT THE ANSWER BUT I ONLY VERIFY​

Answer 1

Question :

The sum of Numerator and Denominator of a fraction is 10. If one is added to both the Numerator and Denominator the fraction becomes ½. Find the fraction.

Given :

• Sum of Numerator and Denominator = 10.

• Fraction when 1 is added to both the Numerator and Denominator = ½.

To find :

The Orginal fraction.

Solution :

Let the Numerator and Denominator of the fraction be a and b, respectively.

Hence, the fraction will be $\bf{\dfrac{x}{y}}$

Now by the given information , we can find two Equations and by solving them, we can find the required value :

Equation i :

Given , the sum of the Numerator and Denominator is 10. i.e,

$\boxed{\therefore \bf{x + y = 10}}$

Where :

• x = Numerator
• y = Denominator

Equation ii :

Orginal Fraction (In terms of x and y) = $\bf{\dfrac{x}{y}}$.

According to the Question, when 1 is added to both the Numerator and Denominator, the fraction becomes ½.i.e,

$\bf{\dfrac{x + 1}{y + 1} = \dfrac{1}{2}}$

By solving it , we get :

$:\implies \bf{2(x + 1) = (y + 1)}$

$:\implies \bf{2x + 2 = y + 1}$

$:\implies \bf{2x - y = 1 - 2}$

$:\implies \bf{2x - y = -1}$

$:\implies \boxed{\therefore \bf{x - y = -1}}$

Where :

• x = Numerator
• y = Denominator

Now by adding Eq.(i) and Eq.(ii) , we get :

$:\implies \bf{(x + y) + (2x - y) = 10 + (-1)}$

$:\implies \bf{x + y + 2x - y = 10 - 1}$

$:\implies \bf{x + \not{y} + 2x - \not{y} = 10 - 1}$

$:\implies \bf{x + 2x = 9}$

$:\implies \bf{3x = 9}$

$:\implies \bf{x = \dfrac{9}{3}}$

$:\implies \bf{x = \dfrac{\not{9}}{\not{3}}}$

$:\implies \bf{x = 3}$

$\boxed{\therefore \bf{x = 3}}$

Hence, the value of x is 3.

Now putting the value of x in Eq.(i) we get :

$:\implies \bf{x + y = 10}$

$:\implies \bf{3 + y = 10}$

$:\implies \bf{y = 10 - 3}$

$:\implies \bf{y = 7}$

$\boxed{\therefore \bf{y = 7}}$

Hence, the value of y is 7.

Since, we have taken x as the Numerator and y as the Denominator, the orginal Fraction is 3/7.

Answer 2

Question :

The sum of Numerator and Denominator of a fraction is 10. If one is added to both the Numerator and Denominator the fraction becomes ½. Find the fraction.

Given :

Sum of Numerator and Denominator = 10.

Fraction when 1 is added to both the Numerator and Denominator = ½.

To find :

The Orginal fraction.

Solution :

Let the Numerator and Denominator of the fraction be a and b, respectively.

Hence, the fraction will be

Now by the given information , we can find two Equations and by solving them, we can find the required value :

Equation i :

Given , the sum of the Numerator and Denominator is 10. i.e,

Where :

x = Numerator

y = Denominator

Equation ii :

Orginal Fraction (In terms of x and y) = .

According to the Question, when 1 is added to both the Numerator and Denominator, the fraction becomes ½.i.e,

By solving it , we get :

Where :

x = Numerator

y = Denominator

Now by adding Eq.(i) and Eq.(ii) , we get :

Hence, the value of x is 3.

Now putting the value of x in Eq.(i) we get :

Hence, the value of y is 7.

Since, we have taken x as the Numerator and y as the Denominator, the orginal Fraction is 3/7.