The sum of numerator and denominator of a fraction is 3 less than twice the denominator. If each of the numerator and denominator is decreased by 1, the fraction becomes 12. Find the fraction.
Let the numerator be x and denominator be y.
Let the fraction be xy
x+y+3=2y
(or) x−y=−3
(or) x=y−3 _____ (1)
Also , x−1y−1=12
x−1=y−12
x=y−12+1⇒2x=y−1+2=y+1
(or) 2x−y=1 _____ (2)
substituting (1) in (2),
2(y−3)−y=1
⇒2y−6−y=1⇒y=7
put y=7 in (1) we get x=7−3=4
∴x=4,y=7
∴ the fraction is xy=47