Question

the sum of numerator and denominator of a fraction is 11 if 1 is added to the numerator and 2 is subtracted from the denominator it becomes 2 by 3 find the fraction​

Answer 1

Hey friend..!! here's your answer

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Let the numerator = x

denominator = y

According to question,

x + 1 / y + 1 = 2 / 3

3x + 3 = 2y + 2

3x - 2y = -1 ----------------1

x - 1 / y - 1 = 3 / 5

5x - 5 = 3y - 3

5x - 3y =2 ------------------2

We get 2 question , Now by Elimination Method ,

3x - 2y = -1 × 5

5x - 3y = 2 × 3

15x - 10y = -5

15x - 9y = 6

- + -

__________

-y = -11

y = 11

Now put the value of in equation 1

3x - 2(11) = - 1

3x - 22 = -1

3x = 21

x = 7

So that the value of x is and y is 11.

We know numerator = x and denominator = y

Numerator / Denominator = 7 / 11

So that the fraction is 7 / 11

$\huge \bold \green{hope \: it \: helps |?| }$

Answer 2

SOLUTION:-

sum of numerator and denominator in a fraction:-11

n+d=11

if 1 is added to the numerator and 2 is subtracted from the denominator, it becomes 2/3.

$\frac{n+1}{d-2}=\frac{2}{3}$

Cross multiply:-

3(n+1) = 2(d-2)

3n + 3 = 2d - 4

3n = 2d - 4 - 3

3n = 2d - 7

replace n with (11-d)

3(11-d) = 2d - 7

33 - 3d = 2d - 7  

33 + 7 = 2d + 3d

40 = 5d

d = 40/5

d = 8

then

n = 11 - 8

n = 3

$\frac{3}{8}$