Question

The sum of numerator and denominator
of a
centain fraction is 8. If 2 is
added to the numerator and to the denominator,
the value.What is the answer?
​

Answer 1

Answer:

Let numerator be x

denominator be 8-x

ATQ

$\frac{x + 2}{8 - x + 2} = \frac{x + 2}{10 + x}$

Answer 2

Correct Question = The sum of numerator and denominatorof a certain fraction is 8. If 2 is added to the numerator and to the denominator, the value of the fraction is increased by 4/35. Find the fraction.​

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assumption

Denominator be t

Also,

Numerator be p

So,

Fraction = p/t

Situation,

First,

p + t = 8

p = 8 - t ..................(1)

2nd Part,

(p + 2)/(t + 2) = p/t + 4/35

(8 - t + 2)/(t + 2) = (8 - t)/t + 4/35

(10 - t)/(t + 2) = 35(8 - t) + 4t/35t

35t(10 - t) = (t + 2)(280 - 31t)

-35t² + 31t² + 350t - 280t + 62t - 560 = 0

t² - 33t + 140 = 0

t² - 28t - 5t + 140 = 0

t(t - 28) - 5(t - 28) = 0

(t - 28) (t - 5) = 0

t = 28 or t = 5

Substitute the value of t in (1) we get,

p = 8 - t

p = 8 - 28

p = -20 (Negative value is not applicable)

Also,

p = 8 - 5

p = 3

Also, t = 5

Therefore,

Required fraction = 3/5