Question

If we add 1 to the numerator and subtract 1 to the denominator, a fraction reduces to 1. It becomes ½ if we only add 1 to the denominator. What is the fraction

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• If we add 1 to the numerator and subtract 1 from the denominator, the fraction becomes 1.

• If we add 1 to the denominator .the fraction becomes ½.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The original fraction.

$\bf{\underline{\underline\green{Solution:-}}}$

Let the numerator be x

And denominator be y

According the the 1st condition:-

If we add 1 to the numerator and subtract 1 from the denominator, the fraction becomes 1.

If 1 added to the numerator

The numerator = x + 1

If 1 is subtracted from denominator

The denominator = y - 1

The fraction becomes 1

$\rm \implies \dfrac{x + 1}{y - 1} = 1$

By cross multiplication:-

$\rm \implies {x + 1} = {1(y - 1)}$

$\rm \implies {x + 1} = {y - 1}$

$\rm \implies {x - y} = { - 1- 1}$

$\rm \implies {x - y} = { - 2......(i)}$

According the the 2nd condition:-

If we add 1 to only the denominator the fraction becomes ½.

The numerator = x

If 1 is added to denominator

The denominator = y + 1

The fraction becomes ½

$\rm \implies \dfrac{x}{y + 1} = \dfrac{1}{2}$

By cross multiplication:-

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

$\rm \implies {2x} = {y + 1}$

$\rm \implies {2x - y} = {1}......(ii)$

Subtracting equation (i) from (ii)

$\rm \implies {2x - y} - (x - y) = {1} - ( - 2)$

$\rm \implies {2x - y} - x + y = {1} + 2$

$\rm \implies x = 3$

Substituting x = 3 in equation (i)

$\rm \implies x - y= - 2$

$\rm \implies 3 - y= - 2$

$\rm \implies - y= - 2 - 3$

$\rm \implies - y= - 5$

$\rm \implies y= 5$

The numerator = x = 3

The denominator = y = 5

$\underline{\boxed{ \purple{\rm \therefore The \: fraction \: = \frac{3}{5} }}}$