Question

A fraction is such that, if the numerator is multiplied by 3 and the denominator is reduced by 3, we get 18 by 11; but if the numerator is increased by 8 and the denominator is doubled, we get 2 by 3. Find the fraction​

Answer 1

Answer:

Let the fraction be

y

x

Then, according to the given conditions, we have

y−3

3x

=

11

18

and

2y

x+8

=

5

2

⇒11x−6y−18 and 5x+40=4y

⇒11x−6y+18=0 and 5x−4y+40=0

By cross-multiplication, we have

(−6)×40−(−4)×18

x

=

11×40−5×18

−y

=

11×(−4)−5×(−6)

1

⇒

−240+72

x

=

440−90

−y

=

−44+30

1

⇒

−168

x

=

−350

y

=

−14

1

⇒x=

−14

−168

and y=

−14

−350

⇒x=12 and y=25

Hence, the fraction is

25

12

.

Step-by-step explanation:

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