Question

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

Answer 1

Answer :

The original number is $\dfrac{15}{22}$

Step-by-step explanation :

Let the number be x.

Given -

The numerator when increased by 17 = x + 17.

The denominator will be x + 7.

The denominator when decreased by 6 = x + 7 - 6 = x + 1.

This must be equal to 2.

So,

$\sf\\ \\ \implies \dfrac{x + 17}{x + 1} = 2\\ \\ \implies x+17=2(x + 1)\\ \\ \implies x+17=2 x+ 2\\ \\ \implies 2x-x =17 - 2\\ \\ \implies x = 15$

Hence,

The numerator = x = 15.

As given,

The denominator is greater than its numerator by 7.

So,

The denominator = x + 7 = 15 + 7 = 22

The fraction is = $\dfrac{15}{22}$

∴ The original number is $\dfrac{15}{22}$

Answer 2

Answer:

Original number

15/22

Step-by-step explanation:

Let the numerator be a

then the denominator will be a+7

original number is a/( a + 7 )

According to question

( a + 17 )/( a + 7 - 6 ) = 2

( a + 17 )/( a + 1 ) =2

a + 17 = 2( a + 1 )

a + 17 = 2a + 2

a - 2a = 2 - 17

-a = -15

both sides ( - ) cancel

a = 15

therefore numerator a = 15

denominator a + 7 = 15 + 7 = 22

Hence original number is

a/( a + 7 ) = 15/22.