Question

The denominator of a rational number is greater than its numerator by 7 if 3 is subtracted from the numerator and 2 is added to the numerator the new number 1\5 find the rational number​

Answer 1

Answer:

6/13 is the original rational number

Step-by-step explanation:

Numerator = x

x/x+7 = original rational number.

x - 3/ x + 9 = 1/5 = new rational number

5x - 15 = x + 9

4x = 24

x = 24/4

x = 6

x/x+7 = 6/6+7 = 6/13

Original rational number is 6/13

Answer 2

Given,

• The Denominator of a Rational Number is greater than its numerator by 7 .
• If 3 is subtracted from the Numerator and 2 is added to the numerator then the new number is 1/5.

To Find,

• The Fraction

Solution :

$\implies$ Suppose the Numerator be a

And,Suppose the Denominator be b

$\mapsto \underline{\sf{\pink{According \ to \ the \ First \ Condition :}}}$

• The Denominator of a Rational Number is greater than its numerator by 7.

$\longrightarrow \boxed{\sf{b = a + 7}}$    1)Equation

$\mapsto \underline{\sf{\pink{According \ to \ the \ Second \ Condition :}}}$

• If 3 is subtracted from the Numerator and 2 is added to the numerator then the new number is 1/5.

$\implies \sf{\dfrac{a - 3}{b + 2} = \dfrac{1}{5}}$

$\implies \sf{5(a - 3) = b + 2}$

$\implies \sf{5a - 15 = b + 2}$

$\implies \sf{5a - b = 15 + 2}$

$\implies \sf{5a - b = 17}$

$\implies \sf{5a -(a + 7) = 17}$

$\implies \sf{5a - a - 7 = 17}$

$\implies \sf{4a = 17 + 7}$

$\implies \sf{4a = 24}$

$\implies \sf{a = \dfrac{24}{4}}$

$\implies \boxed{\sf{a = 6}}$

Now Put the Value of a in First Equation :-

$\implies \sf{b = a + 7}$

$\implies \sf{b = 6 + 7}$

$\implies \boxed{\sf{b = 13}}$

Therefore,

$\boxed{\sf{\red{The \ Fraction = \dfrac{a}{b} = \dfrac{6}{13}}}}$

$\rule{200}2$