A fraction becomes 2 when 1 is added to both the numerator and the den

1.	A fraction becomes 2 when 1 is added to both the numerator and the denominator, and it becomes 3 when 1 is subtracted from both the numerator and the denominator. The numerator of the given fraction is (a) 7 (b) 4 (c) 3 (d) 2
Answer» (a) 7 Let the fraction be \(\frac{X}{y}\) Given, \(\frac{X+1}{y+2}\)= 2 \(\Rightarrow\) x +1 = 2y + 2 \(\Rightarrow\) x – 2y = 1 ..........(i) and \(\frac{X-1}{y-1}\) = 3 \(\Rightarrow\) x – 1 = 3y – 3 \(\Rightarrow\)x – 3y = –2 ........(ii) Now solve eqn (i) and (ii) for x and y.

A fraction becomes 2 when 1 is added to both the numerator and the denominator, and it becomes 3 when 1 is subtracted from both the numerator and the denominator. The numerator of the given fraction is (a) 7 (b) 4 (c) 3 (d) 2

Answer»

(a) 7

Let the fraction be \(\frac{X}{y}\)

Given, \(\frac{X+1}{y+2}\)= 2

\(\Rightarrow\) x +1 = 2y + 2

\(\Rightarrow\) x – 2y = 1 ..........(i)

and \(\frac{X-1}{y-1}\) = 3

\(\Rightarrow\) x – 1 = 3y – 3 \(\Rightarrow\)x – 3y = –2 ........(ii)

Now solve eqn (i) and (ii) for x and y.