The denominator of a rational number is greater than its numerator by

1.	The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to the denominator the new number becomes 1/5. Then the original number was ……………A) 7/11B) 3/5C) 5/8D) 4/7
Answer» Correct option is (C) 5/8 Let the original rational number is \(\frac xy.\) According to first condition, we have y = x + 3 ___________(1) According to second condition, we have \(\frac{x-3}{y+2}=\frac15\) \(\Rightarrow\) 5x - 15 = y + 2 (By cross multiplication) \(\Rightarrow\) 5x - 15 = (x + 3) + 2 (From (1)) \(\Rightarrow\) 5x - x = 15 + 5 \(\Rightarrow\) 4x = 20 \(\Rightarrow\) x = \(\frac{20}4\) = 5 \(\therefore\) y = 5+3 = 8 (From (1)) \(\therefore\) Original number \(=\frac xy=\frac58.\) Correct option is C) 5/8

The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to the denominator the new number becomes 1/5. Then the original number was ……………A) 7/11B) 3/5C) 5/8D) 4/7

Answer»

Correct option is (C) 5/8

Let the original rational number is \(\frac xy.\)

According to first condition, we have

y = x + 3 ___________(1)

According to second condition, we have

\(\frac{x-3}{y+2}=\frac15\)

\(\Rightarrow\) 5x - 15 = y + 2 (By cross multiplication)

\(\Rightarrow\) 5x - 15 = (x + 3) + 2 (From (1))

\(\Rightarrow\) 5x - x = 15 + 5

\(\Rightarrow\) 4x = 20

\(\Rightarrow\) x = \(\frac{20}4\) = 5

\(\therefore\) y = 5+3 = 8 (From (1))

\(\therefore\) Original number \(=\frac xy=\frac58.\)

Correct option is C) 5/8