Question

7. The denominator of a fraction is 1 more than twice its numerator. If the numerator and
denominator are both increased by 5, it becomes 3/5. Find the original fraction.

Answer 1

Answer:

hey mate!!

original fraction = 7/15

Step-by-step explanation:

Let the numerator = x

Denominator = 2x +1

then,

O. F = x / 2x +1

and then both num.... and deno.... is increased by 5, it becomes 3/5

x+5 / 2x + 1 + 5 = 3/5

x + 5 / 2x + 6 = 3/5

5( x + 5 ) = 3( 2x + 6)

5x + 25 = 6x - 5x

7 = x

x = 7 , we get

O. F = 7 / 2× 7 + 1

= 7/15

hope its help you

Answer 2

Given :-

• The denominator of a fraction is 1 more than twice its numerator.
• If the numerator and denominator are both increase by 5, it becomes 3/5.

To Find :-

• What is the original number.

Solution :-

Let,

$\mapsto \bf{Numerator =\: x}$

$\mapsto \bf{Denominator =\: 2x + 1}$

Hence, the original fraction will be :

$\leadsto \sf\dfrac{Numerator}{Denominator}$

$\leadsto \sf\bold{\pink{\dfrac{x}{2x + 1}}}$

According to the question :

$\bigstar$ 5 is increase with both numerator and denominator, then the new number is 3/5.

$\implies \sf \dfrac{Numerator + 5}{Denominator + 5} =\: New\: Number$

$\implies \sf \dfrac{x + 5}{2x + 1 + 5} =\: \dfrac{3}{5}$

$\implies \sf \dfrac{x + 5}{2x + 6} =\: \dfrac{3}{5}$

By doing cross multiplication we get,

$\implies \sf 3(2x + 6) =\: 5(x + 5)$

$\implies \sf 6x + 18 =\: 5x + 25$

$\implies \sf 6x - 5x =\: 25 - 18$

$\implies \sf\bold{\purple{x =\: 7}}$

Hence, the required original fraction is :

$\longrightarrow \sf Original\: Fraction =\: \dfrac{x}{2x + 1}$

$\longrightarrow \sf Original\: Fraction =\: \dfrac{7}{2(7) + 1}$

$\longrightarrow \sf Original\: Fraction =\: \dfrac{7}{14 + 1}$

$\longrightarrow \sf\bold{\red{Original\: Fraction =\: \dfrac{7}{15}}}$

${\small{\bold{\underline{\therefore\: The\: original\: fraction\: is\: \dfrac{7}{15}\: .}}}}$