Question

A fraction becomes 1/3 when 2 is subtracted from numerator and it becomes 1/2 when 1 is subtracted from denominator. Find the fraction.

Give full explanation!!!​

Answer 1

A fraction becomes 1/3 when 2 is subtracted from numerator and it becomes 1/2 when 1 is subtracted from denominator. Find the fraction.

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Given that:

Fraction is $\sf{\dfrac{1}{3}}$ = -2

Fraction is $\sf{\dfrac{1}{2}}$ = -1

⠀

Solution:

$\tt\longmapsto{\dfrac{x - 2}{y} =\dfrac{1}{3}}$

$\tt\longmapsto{3(x - 2) = y}$

$\tt\longmapsto{3x - 6 = y}$

$\tt\longmapsto{3x - y = 6}$⠀⠀.........(i)

⠀

$\tt\longmapsto{\dfrac{x}{y - 1} =\dfrac{1}{2}}$

$\tt\longmapsto{2x = y - 1}$

$\tt\longmapsto{2x - y = -1}$⠀⠀.........(ii)

⠀

From (i) and (ii)

$\tt\longmapsto{3x - y = 6}$

$\tt\longmapsto{2x - y = -1}$

$\tt\longmapsto{x = 7}$

⠀

★ We will put the value of x in the eq. (i)

$\tt\longmapsto{3x - y = 6}$

$\tt\longmapsto{3(7) - y = 6}$

$\tt\longmapsto{21 - y = 6}$

$\tt\longmapsto{-y = 6 -21}$

$\tt\longmapsto{-y = -15}$

$\tt\longmapsto{y = 15}$

∴ Fraction

$\tt\longmapsto{\dfrac{7}{15}}$

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Answer 2

GiveN:-

• A fraction becomes 1/3 when 2 is subtracted from numerator.

• It becomes 1/2 when 1 is subtracted from denominator.

To FinD:-

• The required fraction?

Solution:-

Let the numerator be x and the denominator be y. The the fraction will be:

• $\rm{ \dfrac{x}{y} }$

Now according to condition -(1): "A fraction becomes 1/3 when 2 is subtracted from numerator."

$\rm{ \dfrac{x - 2}{y} = \dfrac{1}{3}}$

Cross multiplying,

$\rm{3(x - 2) = y}$

Opening the parentheses,

$\rm{3x - 6 = y}$

$\rm{3x - y = 6}$

This is our first equation....

Now According to condition - (2): It becomes 1/2 when 1 is subtracted from denominator.

$\rm{ \dfrac{x}{y - 1} = \dfrac{1}{2} }$

Cross multiplying,

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

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

This is our second equation....

Subtracting equation (2) from equation (1),

$\rm{3x - y - 2x + y = 6 + 1}$

$\rm{x = 7}$

Then,

$\rm{3(7) - y = 6}$

$\rm{y = 21 - 6}$

$\rm{y = 15}$

Therefore:-

The required fraction is 7 / 15 (Ans)