Question

. The denominator of a fraction is 30 more than the numerator of the fraction. If 10 is added to the numerator of the fraction and the denominator is unchanged, the value of the
resulting fraction becomes 3/5
. Find the original fraction.
​

Answer 1

Answer:

The denominator of a fraction is 30 more than the numerator of the fraction. If 10 is added to the numerator of the fraction and the denominator is unchanged, the value of the resulting fraction becomes 3/5.

Answer 2

Let numerator = x , and denominator = y

Condition 1

The denominator of a fraction is 30 more than the numerator of the fraction.

∴ y = x + 30

→ y - x = 30 ..[i]

Condition 2

If 10 is added to the numerator of the fraction and the denominator is unchanged, the value of the resulting fraction becomes 3/5.

$\therefore , \quad \rm \dfrac{x+10}{y} = \dfrac{3}{5}$

$\dashrightarrow \rm 5(x+10)=3y$

$\dashrightarrow \rm 5x+50=3y$

$\dashrightarrow\bf \boxed{\bf 3y-5x=50} \qquad \qquad ...[ii]$

Solving [i] and [ii] using elimination method.

Multiplying [i] by 3 so that the coefficients of y becomes same in both the equations.

3(y-x=30) → 3y - 3x = 90

__________________

Subtracting [i] from [ii]

3y - 5x = 50

-(3y - 3x = 90)

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-2x = -40

-x = -20

$\boxed{\bf x = 20}$

since, y = x + 30

$\therefore$

y = 20+30

y = 50

Hence, the numerator is 20 and denominator is 50.

Therefore the original fraction is $\sf \dfrac{20}{50}$