Question

The numerator of a fraction is less than its denominator by 1. If the numerator becomes three times and the denominator is increased by 19, the new fraction becomes 1/7. Find the fraction. 7​

Answer 1

Answer :-

• The fraction is 1/2.

To find :-

• The fraction.

Step-by-step explanation :-

Let the denominator of the fraction be "x".

Then :-

• It's numerator will be "x - 1", as the numerator of the fraction is less than it's denominator by 1.

Now, three times the numerator will be :-

• "3 (x - 1)".

And increasing the denominator by 19,

• We get "x + 19".

Given that :-

• If the numerator of the fraction becomes three times and the denominator is increased by 19, the new fraction becomes 1/7.

Therefore,

$\longmapsto\rm \dfrac{3 \: (x - 1)}{x + 19} = \dfrac{1}{7}$

$\longmapsto\rm \dfrac{3x - 3}{x + 19} = \dfrac{1}{7}$

$\longmapsto\rm1 \: (x + 19) = 7 \: (3x - 3)$

$\longmapsto\rm x + 19 = 21x - 21$

$\longmapsto\rm x - 21x = - 21 - 19$

$\longmapsto\rm - 20x = - 40$

$\longmapsto\rm x = \cancel{\dfrac{ - 40}{ - 20}}$

$\longmapsto\rm x = 2$

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Hence, the numerator and denominator of the fraction are :-

$\bf Numerator = x - 1 = 2 - 1 = 1.$

$\bf Denominator = x = 2.$

And :-

• The fraction is 1/2.

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