Question

the denominator of a fractoin is 4 more than the numerator.if 1 is added to the numerator and 2 is added to the denominator the value of the fraction becomes ⅘.Find the original fraction​

Answer 1

✬ Original Fraction = 19/23

Step-by-step explanation:

Given:

• Denominator of a fraction is 4 more than numerator.
• After adding 1 and 2 to numerator & denominator respectively the fraction becomes 4/5.

To Find:

• What is the original fraction ?

Solution: Let the numerator be x and denominator be y. Therefore, Fraction is x/y.

➟ Denominator = 4 more than x

➟ y = x + 4.....(1)

[ Now, adding 1 to x and 2 to y ]

• New numerator = (x + 1)
• New denominator = (y + 2)

∴ New fraction = (x + 1)/(y + 2)

A/q

$\implies{\rm }$ (x + 1)/(y + 2) = 4/5

$\implies{\rm }$ 5(x + 1) = 4(y + 2)

$\implies{\rm }$ 5x + 5 = 4y + 8

$\implies{\rm }$ 5x – 4y = 8 – 5

$\implies{\rm }$ 5x – 4(x + 4) = 3

$\implies{\rm }$ 5x – 4x – 16 = 3

$\implies{\rm }$ x = 3 + 16

$\implies{\rm }$ x = 19

So,

➽ Numerator is x = 19

➽ Denominator is y = 19 + 4 = 23

Hence, the original fraction is x/y = 19/23