A fraction is such that if the numerator is multiplied by 3 and the de

1.	A fraction is such that if the numerator is multiplied by 3 and the denominator is reduced by 3 , we get 18/11 , but if the numerator is increased by 8 and the denominator is doubled , we get 2/5 . Then the fraction is
Answer» The fraction is (12/25) or $\frac{12}{25}$ . Step-by-step EXPLANATION: We are given that a fraction is such that if the numerator is multiplied by 3 and the DENOMINATOR is reduced by 3 , we get 18/11 , but if the numerator is INCREASED by 8 and the denominator is doubled , we get 2/5. Let the numerator of the fraction be $x$ and the denominator of the fraction be y. First condition STATES that if the numerator is multiplied by 3 and the denominator is reduced by 3 , we get 18/11, that means; $\frac{3 \times x}{y-3} = \frac{18}{11}$ $33x=18(y-3)$ $33x=18y-54$ $11x = 6y-18$ $x=\frac{6y-18}{11}$ ------------------ [Equation 1] Second condition states that if the numerator is increased by 8 and the denominator is doubled , we get 2/5, that means; $\frac{x+8}{2y}=\frac{2}{5}$ $5(x+8)=4y$ $5x+40=4y$ $5\times (\frac{6y-18}{11}) +40=4y$ {USING equation 1} $\frac{30y-90}{11} +40=4y$ $\frac{30y-90+440}{11} =4y$ ${30y+350} =11 \times 4y$ ${30y+350} =44y$ $44y-30y=350$ $y=\frac{350}{14} =25$ Now, putting value of y in equation 1, we get; $x=\frac{6y-18}{11}$ $x=\frac{6\times 25-18}{11}$ = $\frac{150-18}{11}$ $x=\frac{132}{11} =12$ Therefore, the fraction is $\frac{12}{25}$ .

A fraction is such that if the numerator is multiplied by 3 and the denominator is reduced by 3 , we get 18/11 , but if the numerator is increased by 8 and the denominator is doubled , we get 2/5 . Then the fraction is

Answer»

The fraction is (12/25) or $\frac{12}{25}$ .

Step-by-step EXPLANATION:

We are given that a fraction is such that if the numerator is multiplied by 3 and the DENOMINATOR is reduced by 3 , we get 18/11 , but if the numerator is INCREASED by 8 and the denominator is doubled , we get 2/5.

Let the numerator of the fraction be $x$ and the denominator of the fraction be y.