Question

If the numerator of a fraction is increased by 2 and the denominator by 1, it becomes 5/8 and if the numerator and denominator of the same fraction are each increased by 1, the fraction becomes 1/2. Find the fraction.

• A. 2/7
• B. 3/7
• C. 2/5
• D. 4/5
• E. None of these

Answer 1

The correct option is B

3/7

$\text{Let the numerator be x and denominator be y.}\text{Then, the required fraction is}\frac{x}{y}\frac{x+2}{y+1}=\frac{5}{8}\Rightarrow 8x+16=5y+5\Rightarrow 8x-5y=-11.................\left(i\right)and\frac{x+1}{y+1}=\frac{1}{2}\Rightarrow 2x+2=y+1\Rightarrow 2x-y=-1......................\left(ii\right)\text{On multiplying (i) by 2 and (ii) by 8, we get}16x-10y=-2216x-8y=-8\frac{(-)(+)(+)}{-2y=-14}Ory=7\text{On substituting value of y in equation (ii) , we get}2x-y=-1\Rightarrow 2x=6\Rightarrow x=3\text{Hence, the required fraction is}\frac{3}{7}.$