Question

The denominator of a rational number is 7 more than its numerator. If the numerator is increased by 17,
denominator is decreased by 6 and the new number becomes 2. Find the rational number.

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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

Then, this must be equal to 2.

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  

Step-by-step explanation:

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Answer 2

Given :

• The denominator of a rational number is 7 more than its numerator.
• If the numerator is increased by 17,
• denominator is decreased by 6 and the new number becomes 2.

To find :

• The rational number.

Solution :

Consider,

• Numerator of the rational number = x
• Denominator of the rational number = y

According to the 1st condition :-

• The denominator of a rational number is 7 more than its numerator.

$\to\sf{y=x+7..............(1)}$

According to the 2nd condition :-

• If the numerator is increased by 17, denominator is decreased by 6 and the new number becomes 2.

$\to\sf{\dfrac{x+17}{y-6}=2}$

$\to\sf{\dfrac{x+17}{x+7-6}=2\:[put\:y=x+7\: from\:eq(1)]}$

$\to\sf{\dfrac{x+17}{x+1}=2}$

$\to\sf{2x+2=x+17}$

$\to\sf{2x-x=17-2}$

$\to\sf{x=15}$

• Numerator = 15

Now , put x = 15 in eq(1) for getting the value of y.

$\to\sf{y=x+7}$

$\to\sf{y=15+7}$

$\to\sf{y=22}$

• Denominator = 22

Therefore,

Rational number = $\bold{\dfrac{15}{22}}$