Question

The sum of numerator and denominator of a fraction is 12 if the denominator is increased by b3 the fraction become ½ then the fraction
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Answer 1

Step-by-step explanation:

Given:the sum of numerator and denominator of a fraction is 12.If the denominator is increased by 3 the fraction becomes 1/2

Answer 2

Question:

The sum of numerator and denominator of a fraction is 12 if the denominator is increased by 3 the fraction become ½ then the fraction.

Required answer:

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{5}{7}$

Solution:

Let the numerator be 'x'

Denominator be 'y'

x + y = 12.........(1)

$\: \: \: \: \: \frac{x}{y + 3} = \frac{1}{2}$

2x = y + 3

2x - y = 3.......(2)

multiple equation (1) by 2 = 2x + 2y = 24

(-) (-) (-)

multiple equation (2) by 1 = 2x - y = 3

3y = 21

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = \frac{21}{3} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 7$

Substitute y value in equation (1)

x + 7 = 12

x = 12 - 7

x = 5

$hence \: \frac{x}{y} = \frac{5}{7}$

It's confusing but I will verify it.

x + y = 12

Substituting x value and y value to verify

5 + 7 = 12

12 = 12

L.H.S = R.H.S

Hence, verified