Question

A fraction becomes 1/2 if 2 is added to the numerator and 5 is added to the denominator. It also becomes 1/3 if 2 is subtracted from both the numerator and denominator. Then the fraction is

• A. 3/5
• B. 1/7
• C. 8/15
• D. 4/17

Answer 1

Answer:

A. 3/5

$\frac{3+2}{y+5}=\frac12,$ $2x+4=y+5$

$\frac{x-2}{y-2}=\frac13,$ $3x-6=y-2$

$2x-y=1$

$3x-y=4$

adding these two

$x=3$

$2\times 3+4=y+5$

$10=y+5$

$y=5$

so the fraction is 3/5