Question

The denominator of a rational number is greater than its numerator by 7. If the numerator is increased by 17 and the denominator decreased by 6, the new number becomes 2. Find the original number
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Answer 1

Answer:

15/22

Step-by-step explanation:

Let the denominator be 'x' and the numerator be x.    Thus, fraction be x/y.

As given, denominator  is greater than its numerator by 7.

           ⇒ y = x + 7    ⇒ y - 7 = x

If the numerator is increased by 17 and the denominator decreased by 6, the new number becomes 2. New numerator = x + 17  & new denominator = y - 6  

⇒ (x + 17)/(y - 6) = 2

⇒ x + 17 = 2y - 12

⇒ y - 7 + 17 = 2y - 12

⇒ - 7 + 17 + 12 = 2y - y

⇒ 22 = y

             hence, 22 - 7 = x = 15

∴ Required fraction is x/y = 15/22

Answer 2

Answer:

Given :-

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

To Find :-

• What is the original number.

Solution :-

Let, the numerator be x

And, the denominator will be x + 7

Then, the original number is $\sf \dfrac{x}{x + 7}$

According to the question :

$\implies \sf \dfrac{x + 17}{x + 7 - 6} =\: 2$

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

By doing cross multiplication we get :

$\implies \sf 2(x + 1) =\: x + 17$

$\implies \sf 2x + 2 =\: x + 17$

$\implies \sf 2x - x =\: 17 - 2$

$\implies \sf\bold{\purple{x =\: 15}}$

Hence, the required original number is :

$\longmapsto \sf \dfrac{x}{x + 7}$

$\longmapsto \sf \dfrac{15}{15 + 7}$

$\longmapsto \sf\bold{\red{\dfrac{15}{22}}}$

$\sf\boxed{\bold{\green{\therefore The\: original\: number\: is\: \dfrac{15}{22}.}}}$