Question

a fraction becomes 9/11 7 if 2 is added to both numerator and denominator if 1 is subtracted to more than number and discriminator it become 3 by 2 find the fraction​

Answer 1

Answer:

Let the fraction be x/y.

(x+2)/(y+2) = 9/11, or

9y+18 = 11x+22

9y = 11x+4, or

45y = 55x+20 …(1)

(x+3)/(y+3) = 5/6, or

5y+15 = 6x+18, or

5y = 6x+3, or

45y = 54x+27 …(2)

Equate (1) and (2)

55x+20 = 54x+27

x = 7

Again, 9y = 11x+4, or

9y = 77 + 4 or

y = 81/9 = 9

The fraction is (7/9). Answer

Answer 2

To find the fraction.

EXPLANATION.

Case = 1.

Let the numerator of the fraction be = ( x + 2 )

Let the denominator of the fraction be = ( y + 2 )

Fraction become = 9/11

=> x + 2 / y + 2 = 9/11

=> 11 ( x + 2 ) = 9 ( y + 2 )

=> 11x + 22 = 9y + 18

=> 11x - 9y = -4 .........(1)

Case = 2.

if 1 is subtracted to both numerator and

denominator it become 3/2

=> x - 1 / y - 1 = 3/2

=> 2 ( x - 1 ) = 3 ( y - 1 )

=> 2x - 2 = 3y - 3

=> 2x - 3y = -1 .......(2)

From equation (1) and (2) we get,

=> multiply equation (1) by 1

=> multiply equation (2) by 3

we get,

=> 11x - 9y = -4

=> 6x - 9y = -3

=> 5x = -1

=> x = -1/5

put the value of x = -1/5 in equation (1)

we get,

$\sf : \implies \: 11 \times \dfrac{( - 1)}{5} - 9y = - 4 \\ \\ \sf : \implies \: \frac{ - 11}{5} - 9y = - 4 \\ \\ \sf : \implies \: - 9y = - 4 + \frac{11}{5} \\ \\ \sf : \implies \: - 9y = \frac{ - 20 + 11}{5} \\ \\ \sf : \implies \: - 9y = \frac{ - 9}{5} \\ \\ \sf : \implies \: y \: = \frac{1}{5}$

Therefore,

$\sf : \implies \: fraction \: = \dfrac{x}{y} \\ \\ \sf : \implies \: \frac{ \frac{ - 1}{5} }{ \frac{1}{5} } = \frac{ - 1}{5} \times \frac{5}{1} = \frac{ - 1}{1}$

Fraction = -1/1.