Question

A fraction becomes 4/5 if 1 is added to both numerator and denominator.If however 5 is subtracted from both numerator and denominator the fraction becomes 1/2,what is the fraction

Answer 1

$hi...$
Let the numerator be x and denominator be y.

By the given condition ,

$\frac{x + 1}{y + 1} = \frac{4}{5}$
$5(x + 1) = 4(y + 1)$

$5x + 5 = 4y + 4$

$5x - 4y = 4 - 5$
$5x - 4y = - 1...............(1)$
By the 2nd given condition,

$\frac{x - 5}{y - 5} = \frac{1}{2}$

$2(x - 5) = 1(y - 5)$

$2x - 10 = y - 5$

$2x - y = - 5 + 10$

$2x - y = 5..............(2)$
[Multiplying equation no. (2) by 4]

$8x - 4y = 20..............(3)$
[Subtracting equation no. (3) from (1)]

$5x - 4y = - 1$
$8x - 4y = 20$
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-3x = -21
3x = 21
x = 21 / 3
x = 7

Now ,
Substitute x = 7 in equation no. (2)

2x - y = 5
2(7) - y = 5
14 - y = 5
14 - 5 = y
y = 9

Solution :
x = 7 & y = 9
_________________________
Final Answer :
Required Fraction
$= \frac{x}{y} = \frac{7}{9}$
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$hope \: this \: helps...$

Answer 2

Answer:

The fraction is 7/9

Step-by-step explanation:

I hope this answer helps you.....