Question

In a given fraction if the numerator is multiplied by 2 and the denominator is reduced by 5 we get 6/5but the numerator of the given fraction is inc. by 8 and the denominator is doubled we get 2/5 find the fraction

Answer 1

AnswEr:-

Determined fraction = 12/25

$\rule{200}{1}$

1st case:-

• Numerator × 2 & Denominator -5 =fraction : 6/5

Let the numerator be N & denominator be D.

ATQ:-

➠ 2N/D - 5 = 6/5

➠ 10N = 6(D - 5)

➠ 10N = 6D - 30

➠ N = (6D - 30)/10 -(eq.1)

2nd case:-

• Numerator + 5 & Denominator × 2 = fraction : 2/5

ATQ:-

➠ (N + 8)/2D = 2/5

➠ 4D = 5(N + 8)

➠ 4D = 5N + 40

• From eq.1 :-

➠ 4D = 5[(6D - 30)/10] + 40

➠ 4D = (6D - 30)/2 + 40

➠ 4D = (6D - 30 + 80)/2

➠ 4D = (6D + 50)/2

➠ 8D = 6D + 50

➠ 8D - 6D = 50

➠ 2D = 50

➠ D = 50/2

➠ D = 25

◗Denominator = 25

• Putting value in (eq.1):-

➩ N = [6(25) - 30] /10

➩ N = (150 - 30)/10

➩ N = 120/10

➩ N = 12

◗ Numerator = 12

$\rule{200}{1}$

Fraction:-

⇒ Fraction = N/D

⇒ Fraction = 12/25

$\therefore\underbrace{\textsf{Determined \: fraction = {\textbf{ \dfrac{12}{25} }}}}$

Answer 2

Answer:-

Let , the fraction be x/y.

given that,

If the numerator is multiplied by 2 and the denominator is reduced by 5 we get 6/5.

According to the above situation,

$\frac{2x}{y - 5} = \frac{6}{5}$

After cross multiplication we get,

5(2x) = 6(y - 5)

10x = 6y - 30

$x = \frac{6y - 30}{10} - equation(1)$

And also given that,

If the numerator is increased by 8 and denominator is doubled we get 2/5.

According to this situation,

$\frac{x + 8}{2y} = \frac{2}{5} \\ \\ substitute \: x \: value \: here \\ \\ \frac{ \frac{6y - 30}{10} + 8 }{2y} = \frac{2}{5} \\ \\ \frac{ \frac{6y - 30 + 80}{10} }{2y} = \frac{2}{5} \\ \\ \frac{ \frac{6y + 50}{10} }{2y} = \frac{2}{5}$

After cross multiplication we get,

$5( \frac{6y + 50}{10} ) = 2(2y) \\ \\ \frac{2(3y + 25)}{2} = 4y \\ \\ 3y + 25 = 4y \\ \\ 25 = 4y - 3y \\ \\ y = 25$

Substitute "y" value in equation (1)

$x = \frac{6y - 30}{10} \\ \\ x = \frac{6(25) - 30}{10} \\ \\ x = \frac{120}{10} \\ \\ x = 12$

Hence, the fraction (x/y) is 12/25.