Question

The denominator of a fraction exceeds it's numerator by 7. If two is added to the numerator and 3 is subtracted from the denominator the fraction become 3/5. Find the original fraction.​

Answer 1

Step-by-step explanation:

let the numerator be x

Denominator be x + 4

If the numerator and Denominator increased by 3 then,

The fraction = 4/5

ATP,

$\frac{x + 3}{x + 4 + 3 } = \frac{4}{5}$

$\frac{x + 3}{x + 7} = \frac{4}{5}$

$5(x + 3) = 4(x + 7)$

$5x + 15 = 4 x+ 28$

$5x - 4 x = 28 - 15$

$x = 13$

$\frac{x}{x + 4} = \frac{13}{17}$

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Answer 2

Given:-

• The denominator of a fraction exceeds it's numerator by 7
• If two is added to the numerator and 3 is subtracted from the denominator the fraction become 3/5

To find:-

• The original fraction.

Solution:-

Let the numerator be x and denominator be y

So, fraction is x/y

ATQ,

y = x + 7 --------------> (1)

and

(x+2)/ (y-3) = 3/5 ------------> (2)

Solving eq (2)

5(x+2) = 3(y-3)

=> 5x + 10 = 3y - 9

=> 5x - 3y = 19 -------------.(3)

Solving eq 1 and 3

we get

x = 20

and

y = 27

So fraction is 20/27