Question

1. If 2 is subtracted from numberator and 1 is added to denominator, a
fraction becomes 1/2 but when 4 is added to numerator and 3 is subtracted
from denominator, it becomes 3/2 Find the fraction.
​

Answer 1

Step-by-step explanation:

Let the numerator of fraction be x and denominator of the fraction y.

The fraction is x /y

If 2 is subtracted from the numerator and 1 is added to the denominator, a fraction becomes 1/2

x - 2 / y + 1 = 1/2

2 ( x - 2) = y + 1

2x - 4 = y + 1

2x - y = 4 + 1

2x - y = 5

2x = 5 + y…Eq. 1

when 4 is added to the numerator and 3 is subtracted from the denominator it becomes 3/2.

x + 4/y - 3 = 3/2

2 (x + 4) = 3 (y - 3)

2x + 8 = 3y - 9

2x - 3y = —8 - 9

2x - 3y = —17

2x = 3y - 17…Eq..2

Substituting the value of 2x from Eq..1 to Eq. 2

2x = 5 + y

3y - 17 = 5 + y

3y - y = 5 + 17

2y = 22

y = 22/2

y = 11

The denominator is 11

Substituting the value of y in Eq..2 to derive value of x

2x = 3y - 17

2x = 3 × 11 - 17

2x = 33 - 17

2x = 16

x = 8

The numerator is 8

The fraction is 8/11

Now checking the correctness of answer by substituting the derived value of numerator and denominator

2x = 3y - 17

2 × 8 = 3 × 11 - 17

16 = 33 - 17

16 = 16

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