A fraction becomes 2/3 if its numerator is increased by 1 and denominator by 2.it becomes 3/4 if its numerator is increased by 4 and the denominator by 5. find the fraction.

Answers (1)

Let the fraction 

                             $$fracxy$$\$$

According to 1st condition 

                                $$fracx+1y + 2 = frac23 $$\$$ $$Rightarrow 3(x +1) = 2( y+ 2) $$\$$ $$Rightarrow 3x -2y = 1 .....(1) $$\$$

Now 2nd condition 

                             $$fracx+4y + 5 = frac34 $$\$$ $$Rightarrow 4(x +4) = 3( y+ 5) $$\$$ $$Rightarrow 4x -3y = -1 .....(2) $$\$$

multiply 3 in Equation (1) and 2 in equation (2)

                                             $$ 9x -6y = 3 ....(3) $$\$$ $$ 8x -6y = -2 .....(4) $$\$$

Solve equation (3) and equation (4) we get

                                                                  $$x = 5 and, y = 7 $$\$$

Hence, the fraction 

                                       $$ = frac57 $$\$$

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