Question

In a given fraction, if 1 is subtracted from the numerator and 2 is added to the denominator,it becomes1/2
If 7 is subtracted from the numerator and 2 is subtracted from the denominator, it becomes 1/3.
Then find the fraction
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Answer 1

Answer:-

Let the fraction be x/y.

Given:-

If 1 subtracted from the numerator and 2 is added to the denominator , it becomes 1/2.

$\implies \sf \: \frac{x - 1}{y + 2} = \frac{1}{2} \\ \\ \\ \implies \sf \:2(x - 1) = y + 2 \\ \\ \\ \implies \sf \:2x - 2 = y + 2 \\ \\ \\ \implies \sf \:2x - 2 - 2 = y \\ \\ \\ \implies \sf \:y = 2x - 4 \: \: - - equation \: (1)$

Also given that,

If 7 is subtracted from the numerator and 2 is subtracted from the denominator , it becomes 1/3.

$\implies \sf \: \frac{x - 7}{y - 2} = \frac{1}{3} \\ \\ \\ \implies \sf \:3(x -7) = 1(y - 2)$

Substitute the value of y from equation (1).

$\implies \sf \: 3x - 21 = 2x - 4 - 2 \\ \\ \\ \implies \sf \:3x - 2x = - 4 - 2 + 21 \\ \\ \\ \implies \boxed{\sf \: x = 15}$

Substitute the value of x in equation (1).

⟹ y = 2(15) - 4

⟹ y = 30 - 4

⟹ y = 26

∴ The required fraction x/y = 15/26.

Answer 2

Answer:

Given :-

a given fraction, if 1 is subtracted from the numerator and 2 is added to the denominator,it becomes1/2

If 7 is subtracted from the numerator and 2 is subtracted from the denominator, it becomes 1/3.

To Find :-

Fraction

Solution :-

Let us assume the fraction as x/y

Now,

Numerator decreased by 1 and denominator increased by 2

x - 1/y + 2 = ½

By cross multiplication

⟹ 2(x - 1) = y + 2

⟹ 2x - 2 = y + 2

⟹ 2x - 4 = y (1)

Now,

When 7 subtracted from numerator and 2 subtracted from denominator

⟹ x - 7/y - 2 = ⅓

⟹ 3(x - 7) = y - 2

⟹ 3x - 21 = y - 2

Now,

On using equation 1

⟹ 3x - 21 = 2x - 4 - 2

⟹ 3x - 2x = -4 - 2 + 21

⟹ x = -6 + 21

⟹ x = 15

Now,

⟹ y = 2(15) - 4

⟹ y = 30 - 4

⟹ y = 26

Fraction = 15/26