Question

30. A fraction becomes iif 2 is added to both numerator and denominator. If 3 is added to both
numerator and denominator, it becomes. Find the fraction.
​

Answer 1

Answer:

cpcoycgixifxjfxfjxirxitctixktxktcoydkdyid

Answer 2

Correct Question:

A fraction becomes 9/11 if 2 is added to both numerator and denominator. If 3 is added to both numerator and denominator it becomes 5/6. Find the fraction.

$\huge\mathfrak{Answer:}$

Given:

We have been given that on adding 2 to both numerator and denominator of a fraction, it becomes 9/11.On adding 3 to both numerator and denominator of a fraction, it becomes 5/6.To Find:We need to find the fraction.Solution:Let the numberator be x and denominator be y.

$\mapsto\sf{Fraction = \dfrac{x}{y}}$

Now, according to the question we have

$\sf{ \dfrac{x + 2}{y + 2} = \dfrac{9}{11}}$

On cross multiplying the terms, we have

$\sf{11x + 22 = 9x + 18}11x+22$

$\implies\sf{11x - 9y = 18 - 22}</p><p>$

$\implies \sf{11x - 9y = - 4}</p><p>$

$\implies\sf{11x = 9y - 4}$

Also, when 3 is added to both numerator and denominator, the fraction becomes 5/6. We have

$\sf{\dfrac{x + 3}{y + 3} = \dfrac{5}{6}}$

$\implies\sf{6x + 18 = 5y + 15}$

$\implies\sf{6x - 5y = 15 - 18}$

$\implies\sf{6 \times \dfrac{9y - 4}{11 - 5y} = - 3}$

$\implies\sf{54y - 24 - 55y = - 3}$

$\implies\sf{ - y - 24 = - 3 \times 11}$

$\implies\sf{y + 24 = 33}$

$\implies\sf{y = 33 - 24}$

$\implies\sf{y = 9 }$

When y = 9, therefore

$\sf{x = \dfrac{9 \times 9 - 4}{11}}$

$\implies\sf{x = \dfrac{77}{11}}$

$\implies\sf{x = 7}$

$\mapsto\sf{Fraction = \dfrac{7}{9}}$

Hence, the fraction is 7/9.