Question

There are two fractions such that numerator of second fraction is less by 2 than that the numerator of first fraction. Denominator of second fraction is two times the denominator of first fraction. The sum of two fractions is 7/10 and the difference is 1/2. Find the fractions.​

Answer 1

Step-by-step explanation:

Given There are two fractions such that numerator of second fraction is less by 2 than that the numerator of first fraction. Denominator of second fraction is two times the denominator of first fraction. The sum of two fractions is 7/10 and the difference is 1/2. Find the fractions.

• Let one of the fraction be x / y
• Let the other fraction be x – 2 / 2y
• According to question we get
• x / y + x – 2 / 2y = 7 / 10
• x / y - x – 2 / 2y = 1/2  
• now we have two simultaneous equations, by adding we get
• 2 x / y = 6/5
• 10 x = 6y
• 5x = 3y
• Subtracting the equations we get  
• x – 2 / 2y + x – 2 / 2y = 7/10 – 1/2  
• x – 2 + x – 2 / 3y = 1/5
• x – 2 + x – 2 / 2y = 1/5
• 2x – 4 / 2y = 1/5
• Or y = 5x – 10
• Or y = 3y – 10 (since 5x = 3y)
• Or y = 5
• Now 5x = 3y
• 5x = 3 (5)
• Or x = 3

So the two fractions are 3/5 and 1/10

Reference link will be

https://brainly.in/question/14111772

Answer 2

The fractions are $\frac{3}{5}$ and $\frac{1}{10}$.

Step-by-step explanation:

Let the first fraction is $\frac{x}{y}$, then the second fraction will be $\frac{x - 2}{2y}$ .

{From the conditions given}

Now, $\frac{x}{y} + \frac{x - 2}{2y} = \frac{7}{10}$

⇒ $\frac{2x + x - 2}{2y} = \frac{7}{10}$

⇒ 15x - 10 = 7y

⇒ 15x - 7y = 10 ...........  (1)

Again, we have,

$\frac{x}{y} - \frac{x - 2}{2y} = \frac{1}{2}$

⇒ $\frac{2x - x + 2}{2y} = \frac{1}{2}$

⇒ x + 2 = y ........... (2)

Now, from equations (1) and (2) we get,

15x - 7(x + 2) = 10

⇒ 8x = 24

⇒ x = 3

Now, from equation (2) we get, y = 3 + 2 = 5

Therefore, the fractions are $\frac{3}{5}$ and $\frac{1}{10}$. (Answer)