Question

If numerator is multiplied by 3 and 3 is subtracted from the denominator then the fraction obtained is 18/11 . If numerator is increased by 8 and denominator is doubled then the resulting fraction is 1/2 . Find them. ​

Answer 1

Answer:

Original fraction = 6/14 .

Step-by-step explanation:

Let numerator be x  and  denominator be y.

First condition says that If numerator is multiplied by 3 and 3 is subtracted from the denominator then the fraction obtained is 18/11 i.e.;

                                   $\frac{x*3}{y-3}= \frac{18}{11}$

                                 33 * x = 18(y - 3)

                                 33*x = 18*y - 54

                                 11*x = 6*y - 18 ---------- [Equation 1]

Second condition says that If numerator is increased by 8 and denominator is doubled then the resulting fraction is 1/2, i.e.;

                                  $\frac{x+8}{2y} = \frac{1}{2}$

                               2(x + 8) = 2*y

                                x + 8 = y

                                 x = y - 8 ----------- [Equation 2]

Now, putting value of x from equation 2 into equation 1, we get;

                    11(y - 8) = 6*y - 18

                    11*y - 88 = 6*y - 18

                    11*y - 6*y = 88 - 18

                       5*y = 70

                        y = 14 and so x = 14 - 8 = 6

Therefore, numerator, x = 6  and  denominator, y = 14 .

Answer 2

Answer:

the fraction is 12/25

Step-by-step explanation:

Let the fraction be x/y.

Then,

According to the question

3x/y - 3 = 18/11

and x + 8/2y = 2/5

⇒ 11x = 6y - 18 and 5x + 40 = 4y

⇒ 11x - 6y + 18 = 0 and 5x - 4y + 40 = 0

By cross-multiplication. we get

⇒ x/(- 6) × 40 - (- 4) × 18 = - y/11 × 40 - 5 × 18 = 1/11 × (- 4) - 5 × (- 6)

⇒ x/- 240 + 72 = - y/440 - 90 = 1/- 44 + 30

⇒ x/- 168 = y/- 350 = 1/- 14

⇒ x = - 168/- 14 and y = - 350/- 14

⇒ x = 12 and y = 25

Hence, the fraction is 12/25