Question

If the numerator of a fraction in increased by 2 and the denominator is increased by 1, the fraction becomes $\frac{5}{8}$ and if the numerator of the same fraction is increased by 3 and the denominator is increased by 1 the fraction becomes $\frac{3}{4}$ what is the original fraction?

• A. Data inadequate
• B. $\frac{1}{7}$
• C. $\frac{2}{7}$
• D. $\frac{3}{7}$

Answer 1

The correct option is D $\frac{3}{7}$

Let the original fraction be $\frac{x}{y}$
Then, $\frac{x+2}{y+1}=\frac{5}{8}or,8x-5y=-11$ . . . (i)
Again, $\frac{x+3}{y+1}=\frac{3}{4}or,4x-3y=-9$ . . . (ii)
Solving, we get x = 3 and y = 7
Fraction $=\frac{3}{7}$