Question

a fraction becomes 9 upon 11 if 2 is added to both the numerator and denominator if 3 is added to both the numerator and denominator it becomes 5upon6 find the fraction​

Answer 1

SOLUTION:-

Given:

A fraction becomes 9/11. If 2 is added to both the numerator & denominator, if 3 is added to both the numerator & denominator it becomes 5/6.

To find:

The fraction.

Explanation:

Let numerator be R.

Let denominator be M.

The fraction will make= R/M.

CASE 1:

A fraction make, & added 2 both the numerator & denominator equal to 9/11.

$= > \frac{R+ 2}{M + 2} = \frac{9}{11} \\ [cross \: multiplication] \\ \\ = > 11R+ 22 = 9M + 18 \\ \\ = > 11R - 9M = 18 - 22 \\ \\ = > 11R- 9M= - 4 \\ \\ = > 11R= - 4 + 9M\\ \\ = > R = \frac{ - 4 + 9M}{11} .....................(1)$

&

CASE 2:

Given that 3 is added to both the numerator & denominator it make a fraction 5/6.

$= > \frac{R+ 3}{M + 3} = \frac{5}{6} \\ [cross \: multiplication] \\ \\ = > 6R+ 18 = 5M + 15 \\ \\ = > 6R- 5M = 15 - 18 \\ \\ = >6R - 5M= - 3 \\ \\ = > 6( \frac{ - 4 + 9M}{11} ) - 5M = -3 \: \: \: \: \: \: \: \: [using \: equation \: (1)] \\ \\ = > \frac{ - 24 + 54M}{11} - 5M = - 3 \\ \\ = > - 24 + 54M - 55M = - 33 \\ \\ = >54 M- 55M = - 33 + 24 \\ \\ = > - M = - 9 \\ \\ = > M = 9$

So,

Putting the value of m in equation (1), we get;

$= > R = \frac{ - 4 + 9(9)}{11} \\ \\ = > R = \frac{ - 4 + 81}{11} \\ \\ = > R = \frac{77}{11} \\ \\ = > R= 7$

Therefore,

The fraction is 7/9.

Thank you.