Question

A denominator of a rational number is greater than its numerator by 7 . numerator is the increased by 17 and the denominator is decreased by 6 the new number becomes 2. find the
orginial number​

Answer 1

Answer:

2

Step-by-step explanation:

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.

Answer 2

Answer:

The Original Fraction = 15/22 .

✳SOLUTION✳

Let us assume that the numerator of the fraction is 'x'.

∵ It is given that the denominator of a rational number is greater than its numerator by 7,

The Denominator will be = x + 7$\longrightarrow$ (1)

Next , it is said that the numerator is the increased by 17 and the denominator is decreased by 6 the new number becomes 2.

$\implies$

$\sf \dfrac{x+17}{x+(7-6)} = 2$

$\implies$

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

$\implies$

x + 17 = 2(x + 1)

$\implies$

x + 17 = 2x + 2

$\implies$

2x - x = 17 - 2

$\implies$

x = 15

∴The numerator of the fraction = 15.

Now , let us substitute the value of x = 15 in (1) to find the denominator of the fraction.

∴ The denominator of the fraction = = 15 + 7 = 22

$\implies$

$\bigstar \tt The \: original \: Fraction = \dfrac{15}{22}$