Question

the denominator of a fraction is 1 less than twice its numerator if 1 is added to numerator and denominator respectively the ratio of numerator to denominator is 3 is to 5 find the fraction

Answer 1

numerator=x
denominator=2x-1
x+1/2x-1+1=3/5
x+1/2x=3/5
5x+5=6x
x=5

Answer 2

The denominator of a fraction is 1 less than twice its numerator if 1 is added to numerator and denominator respectively the ratio of numerator to denominator is 3 is to 5. Then the fraction is $\frac{5}{9}$

Solution:

Let the numerator be "a" and denominator be "b"

Given that denominator of fraction is 1 less than twice its numerator

Hence we get,

b = 2a - 1  ----- eqn 1

Also given that if 1 is added to numerator and denominator respectively the ratio of numerator to denominator is 3 is to 5

Hence we get,

a + 1 : 2a - 1 + 1 = 3 : 5

a + 1 : 2a = 3 : 5

Writing in fraction,

$\frac{a+1}{2 a}=\frac{3}{5}$

5(a+1) = 3(2a)

5a + 5 = 6a

6a – 5a = 5

a = 5

Substituting "a" in eqn 1, we get value of "b"

b = 2a - 1 = 2(5) - 1 = 10 - 1 = 9

Thus b = 9

$\text { So, the fraction is } \frac{a}{b}=\frac{5}{9}$

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