In a fraction the denominator is 6 more than the numerator. If 3 is ad

1.	In a fraction the denominator is 6 more than the numerator. If 3 is added to numerator the fraction equals to 2/3 then the fraction is …………………….. A) 3/9 B) 2/9 C) 2/6 D) 3/6
Answer» Correct option is A) 3/9 Correct option is (A) 3/9 Let the fraction be \(\frac xy.\) Given that denominator (y) is 6 more than the numerator (x). \(\therefore\) y = x+6 _________(1) Also \(\frac{x+3}y=\frac23\) \(\Rightarrow\) 3x+9 = 2y \(\Rightarrow\) 3x+9 = 2(x+6) (From (1)) \(\Rightarrow\) 3x - 2x = 12 - 9 = 3 \(\Rightarrow\) x = 3 Then from (1), we get y = x+6 = 3+6 = 9 \(\therefore\) Given fraction is \(\frac39.\)

In a fraction the denominator is 6 more than the numerator. If 3 is added to numerator the fraction equals to 2/3 then the fraction is …………………….. A) 3/9 B) 2/9 C) 2/6 D) 3/6

Answer»

Correct option is A) 3/9

Correct option is (A) 3/9

Let the fraction be \(\frac xy.\)

Given that denominator (y) is 6 more than the numerator (x).

\(\therefore\) y = x+6 _________(1)

Also \(\frac{x+3}y=\frac23\)

\(\Rightarrow\) 3x+9 = 2y

\(\Rightarrow\) 3x+9 = 2(x+6) (From (1))

\(\Rightarrow\) 3x - 2x = 12 - 9 = 3

\(\Rightarrow\) x = 3

Then from (1), we get

y = x+6 = 3+6 = 9

\(\therefore\) Given fraction is \(\frac39.\)