Question

if 1 is subtracted from the numerator of a fraction it becomes 3 upon 5 but if 5 is added to the denominator of the fraction it becomes 1 upon 2 find the fraction?​

Answer 1

Answer:

10 / 15

Step-by-step explanation:

Let the numerator of the fraction be a and denominator be b.

According to the situation given above, if 1 is subtracted from then numerator it becomes 3 / 5. We have assumed numerator as a, so if 1 is subtracted from a then,

⇒ ( a - 1 ) / b = 3 / 5

⇒ 5( a - 1 ) = 3b

⇒ 5a - 5 = 3b

= > 5a - 3b = 5                ...( 1 )

Situation 2 says if 5 is added to the denominator of the fraction it becomes 1 / 2, we assumed denominator as b, so if 5 is added it becomes b + 5 and fraction becomes 1 / 2.

⇒ a / ( b + 5 ) = 1 / 2

= > 2a = b + 5

= > 2a - b = 5             ...( 2 )

Multiplying both sides of ( 2 ) by 3 : 2a - b = 5       ⇒ 6a - 3b = 15

Now, subtracting ( 1 ) from this :  

   6a - 3b = 15

   5a - 3b = 5

   a          = 10

Therefore,

= > a = 10

= > 2a - b = 5

= > 2( 10 ) - b = 5

= > 20 - 5 = b

= > 15 = b

Hence the given fraction is 10 / 15.

Answer 2

ANSWER:

Let the fraction be $\red{\dfrac{x}{y}}$

Given

• $\dfrac{x - 1}{y} = \dfrac{3}{5}$
• $\dfrac{x}{y + 5} = \dfrac{1}{2}$

Find

• $\frac{x}{y} = ?$

━━━━━━━━━━━━━━━━━

$\huge{\underline{\underline{\red{SOLUTION}}}}$

$\dfrac{x - 1}{y} = \dfrac{3}{5} \\ = > 5x - 5 = 3y \\ = > 5x - 3y = 5 - - - - - i$

━━━━━━━━━━━━━━━━

also given,

$\dfrac{x}{y + 5} = \dfrac{1}{2} \\ = > 2x = y + 5 \\ = > 2x - y = 5$

multiplying both side by 3 we get,

$(2x - y) \times 3 = 5 \times 3 \\ = > 6x - 3y = 15 - - - - ii$

━━━━━━━━━━━━━━━━

By Subtracting i from ii we get;

(6x-3y)-(5x-3y)=15-5

=> 6x-3y-5x+3y=10

=> x= 10-----A

━━━━━━

Now from eq. 1 we know;

5x-3y=5

5×10-3y=5

50-3y=5

3y=50-5

y=45÷3

y=15

Thus

$\dfrac{x}{y} = \dfrac{10}{15}$

$\large{\red{\boxed{\boxed{Fraction=\dfrac{10}{15}}}}}$