Question

25 km?
9
(v) A fraction becomes -, if 2 is added to both the numerator and the denominator.
11
II, 3 is added to both the numerator and the denominator it becomes
Find the
5
6
fraction​

Answer 1

Answer:

Let the numerator and denominator be x and y respectively.

Therefore, the required fraction will be x/y

According to Question now,

➳ (x + 2)/(y + 2) = 9/11

➳ 11(x + 2) = 9(y + 2)

➳ 11x + 22 = 9y + 18

➳ 22 - 18 = 9y - 11x

➳ 4 = 9y - 11x

➳ 11x = 9y - 4

➳ x = 9y - 4/11.......[Equation (i)]

Now, it is given that 3 is added to both numerator and denominator it becomes 5/6 :]

➳ (x + 3)/(y + 3) = 5/6

➳ (x + 3)6 = 5(y + 3)

➳ 6x + 18 = 5y + 15

➳ 6x - 5y + 18 - 15 = 0

➳ 6x - 5y + 3 = 0

➳ 6(9y - 4)/11 - 5y + 3 = 0

➳ 54y - 24/11 = 5y - 3

➳ 54y - 24 = 11(5y - 3)

➳ 54y - 24 = 55y - 33

➳ -24 + 33 = 55y - 54y

➳ 9 = y

Now, Putting y = 9 in equation (i) we get,

➳ x = 9y - 4/11

➳ x = 9(9) - 4/11

➳ x = 81 - 4/11

➳ x = 77/11

➳ x = 7

Therefore, the required fraction is 7/9.

Answer 2

✦ Question ✦

A fraction becomes -, if 2 is added to both the numerator and the denominator.11 II, 3 is added to both the numerator and the denominator it becomesFind the 56 fraction

Answer :-

The Fraction is 7/9.

Given :-

A fraction becomes -, if 2 is added to both the numerator and the denominator.

Calculations :-

Consider the numerator as m

Denominator as n

From this we get our fraction as m/n

Now , let's make an equation and solve it .

We know 2 is added in both numerator and denominator

Which is equal to 9 / 11

So ,

(m + 2)/ (n + 2) = 9/11

Just Simply doing cross multiplication .

$:\implies\pink{\tt{11(m+ 2) = 9(n + 2)</p><p>}}$

$:\implies\pink{\tt{ 11m + 22 = 9n + 18}}$

$:\implies\pink{\tt{22 - 18 = 9n - 11m}}$

$:\implies\pink{\tt{4 = 9n - 11m}}$

$:\implies\pink{\tt{11m = 9n - 4}}$

$:\implies\purple{\tt{m = 9n - 4/11. ...... 1 }}$

Again as per the given :-

(m + 3)/(n + 3) = 5/6

$:\implies\pink{\tt{ (m + 3)6 = 5(n + 3)</p><p>}}$

$:\implies\pink{\tt{ 11m + 22 = 9n + 18}}$

$:\implies\pink{\tt{6m + 18 = 5n + 15}}$

$:\implies\pink{\tt{6m - 5n + 18 - 15 = 0}}$

$:\implies\pink{\tt{6m - 5n + 3 = 0}}$

$:\implies\pink{\tt{6(9n - 4)/11 - 5n + 3 = 0</p><p>}}$

$:\implies\pink{\tt{ 54n - 24/11 = 5n - 3}}$

$:\implies\pink{\tt{54n - 24 = 11(5n - 3)}}$

$:\implies\pink{\tt{54n - 24 = 55n - 33}}$

$:\implies\pink{\tt{ -24 + 33 = 55n - 54n}}$

$:\implies\purple{\tt{ n = 9</p><p> }}$

Therefore substituting the value in the above Equation 1 .

↠ m = 9n - 4/11

↠ m = 9(9) - 4/11

↠ m = 81 - 4/11

↠ m = 77/11

↠ m = 7

Hence ,

The fraction is

$\frac{7}{9}$