Question

The denominator of a rational number is greater than its numerator by 3. If the numerator is increased by 7 and the denominator is decreased by 1, the new number becomes 3/2. Find the original number

Answer 1

Answer:

The original number is 15/22

Solution:

Let us take the numerator to be x.

So, the denominator will be x+7.

Given condition is

The numerator when increased by 17 = x+17

and the denominator when decreased by 6 =x+7-6=x+1=x+7−6=x+1

Then, this must be equal to 2.

\begin{lgathered}\begin{array} { c } { \frac { x + 17 } { x + 1 } = 2 } \\\\ { ( x + 17 ) = 2 ( x + 1 ) } \\\\ { x + 17 = 2 x + 2 } \\\\ { 2 x - x = 17 - 2 } \\\\ { x = 15 } \end{array}\end{lgathered}x+1x+17=2(x+17)=2(x+1)x+17=2x+22x−x=17−2x=15

Thus, the numerator = x = 15.

As per the condition, the denominator is greater than its numerator by 7.

And, the denominator = x+7 = 15+7 = 22

So, the fraction is =15/22    

Thus, the original number is the fraction of 15/22 

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Answer 2

Let the numerator of the rational number be x. Therefore, its denominator will be x + 8. The rational number will be x/x + 8. According to the question, x + 17/x + 8 - 1 = 3/2 ⇒ x + 17/x + 7 = 3/2 ⇒ 2(x + 17) = 3(x + 7) ⇒ 2x + 34 = 3x + 21 ⇒ 34 − 21 = 3x − 2x ⇒13 = x Numerator of the rational number = x = 13 Denominator of the rational number = x + 8 = 13 + 8 = 21 Rational number = 13/21

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