Question

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 1

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  $\frac{12}{25}$ .

Answer 2

Answer:

Ur answer is in the attachment..

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