Question

A fraction is such that if the numerator is multiplied by3 and denominator is reduced by 3, we get 18/11, but if the numerator is increased by8 and denominator is doubled ,we get 2/5. Find the fraction.

Answer 1

Answer:

Step-by-step explanation:

Given,

• A fraction is such that if the numerator is multiplied by 3 and denominator is reduced by 3, we get 18/11.
• But if the numerator is increased by 8 and denominator is doubled ,we get 2/5.

To Find,

• The fraction

Solution,

Let the fraction be x/y.

Then,

According to the question

3x/y - 3 = 18/11and 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.

Answer 2

★ Solution :-

Let the numerator be x.

Let the denominator be y.

So, the fraction is

$\sf \leadsto \dfrac{x}{y}$

According to the first case,

$\sf \leadsto \dfrac{3x}{y - 3} = \dfrac{18}{11}$

$\sf \leadsto 11(3x) = 18(y - 3)$

$\sf \leadsto 33x = 18y - 54$

$\sf \leadsto 33x - 18y = -54 \: --- (i)$

According to the second case,

$\sf \leadsto \dfrac{x + 8}{2y} = \dfrac{2}{5}$

$\sf \leadsto 5(x + 8) = 2(2y)$

$\sf \leadsto 5x + 40 = 4y$

$\sf \leadsto 5x - 4y = -40 \: \: --- (ii)$

By first equation,

$\sf \leadsto 33x - 18y = -54$

$\sf \leadsto 33x = -54 + 18y$

$\sf \leadsto x = \dfrac{-54 + 18y}{33}$

Now, we can find the value of y by second equation.

$\sf \leadsto 33x - 18y = -54$

$\sf \leadsto 33 \bigg( \dfrac{-54 + 18y}{33} \bigg) - 4y = -40$

$\sf \leadsto \dfrac{-1782 + 594y}{33} - 4y = -40$

$\sf \leadsto \dfrac{-1782 + 594y - 132y}{33} = -40$

$\sf \leadsto \dfrac{-1782 + 462y}{33} = -40$

$\sf \leadsto -1782 + 462y = -40 \times 33$

$\sf \leadsto -1782 + 462y = -1320$

$\sf \leadsto 462y = -1320 + 1782$

$\sf \leadsto 462y = 462$

$\sf \leadsto y = \dfrac{462}{462}$

$\sf \leadsto y = 1$

Now, we can find the value of x by first equation.

$\sf \leadsto 33x - 18y = -54$

$\sf \leadsto 33x - 18(1) = -54$

$\sf \leadsto 33x - 18 = -54$

$\sf \leadsto 33x = -54 + 18$

$\sf \leadsto 33x = -36$

$\sf \dashrightarrow x = \dfrac{-36}{33}$

$\sf \leadsto x = \dfrac{-12}{11}$

Value of x :- -12/11

Value of y :- 1

Therefore, the fractions $\sf \dfrac{-12}{11}$.