Question

The denominator of a fraction is 3 more than the numerator. If 5 is added to both parts, the resulting
fraction is equivalent to 4/5Find the fraction
​

Answer 1

$\bf{\huge{\underline{\boxed{\sf{\red{Answer:}}}}}}$

$\bf{\underline{\underline{\sf{\blue{Given:}}}}}$

• The denominator of a fraction is 3 more than the numerator.
• If 5 is added to both parts, the resulting fraction is equivalent to $\frac{4}{5}$

$\bf{\underline{\underline{\sf{\blue{To\:find\::}}}}}$

• The fraction.

$\bf{\underline{\underline{\sf{\blue{Solution\::}}}}}$

Let the Numerator of the fraction be x.

Let the denominator of the fraction be y.

Fraction = $\bf\frac{x}{y}$

$\bf{\underline{\underline{\sf{\green{As\:per\:first \:condition\::}}}}}$

• The denominator of a fraction is 3 more than the numerator

Representing the condition mathematically to obtain our first equation.

=> y = x + 3

=> x + 3 = y

=> x - y = - 3 ----> 1

$\bf{\underline{\underline{\sf{\green{As\:per\:second \:condition\::}}}}}$

• If 5 is added to both parts, the resulting fraction is equivalent to $\frac{4}{5}$

Numerator = x + 5

Denominator = y + 5

Fraction = $\bf\frac{4}{5}$

Representing the second condition mathematically.

=> $\frac{x + 5}{y + 5}$ = $\frac{4}{5}$

Cross multiplying,

=> 5 ( x + 5) = 4 ( y + 5)

=> 5x + 25 = 4y + 20

=> 5x - 4y = 20 - 25

=> 5x - 4y = - 5 ----> 2

Multiply equation 1 by 5,

x - y = - 3 ---> 1

5 × x - 5 × y = 5 × - 3

5x - 5y = - 15 ----> 3

Solve equations 2 and 3 simultaneously by elimination method.

Subtract equation 3 from 2 ,

....+ 5x - 5y = - 15 ----> 3

- ( + 5x - 4y = - 5 )-----> 2

---------------------------

- y = - 10

y = 10

Substitute y = 10 in equation 1,

x - y = - 3

x - 10 = - 3

x = - 3 + 10

x = 7

Numerator, x = 7

Denominator, y = 10

Fraction = $\bf\frac{7}{10}$

$\bf{\huge{\underline{\boxed{\sf{\red{Verification:}}}}}}$

For first case :-

• The denominator of a fraction is 3 more than the numerator

Numerator = x = 7

Denominator = y = 10

=> y = x + 3

=> 10 = 7 + 3

=> 10 = 10

LHS = RHS.

For second case :-

• If 5 is added to both parts, the resulting fraction is equivalent to $\frac{4}{5}$

Numerator = x + 5 = 7 + 5 = 12

Denominator = y + 5 = 10 + 5 = 15

=> $\frac{x + 5}{y + 5}$ = $\frac{4}{5}$

=> $\frac{12}{15}$ = $\frac{4}{5}$

Dividing LHS by 3,

=> $\frac{4}{5}$ = $\frac{4}{5}$

LHS = RHS.

Hence verified.

Answer 2

Answer:

here your answer.......

7/10.

Step-by-step explanation:

let the numerator be x

then the denominator will be x+3

According to question

x+5/x+3+5=4/5

x+5/x+8=4/5

5(x+5)=4(x+8)

5x+25=4x+32

5x-4x=32-25

x=7

denominator is x+3=7+3=10

the numerator 7

and

denomirator 10

therefore the fraction is 7/10.