Question

If 1 is subtracted from the numerator and from the denominator of a fraction , the value obtained is 1/2 . If 1 is added to its numerator and to its denominator , the resulting value is 2/3. How do we find the fraction?

Answer 1

Your answer is in the attachment ✌️

Hope it helps you :-) ♥️

Answer 2

$\star\:\:\:\bf\large\underline\blue{Question:-}$

• If 1 is subtracted from the numerator and from the denominator of a fraction , the value obtained is 1/2 . If 1 is added to its numerator and to its denominator , the resulting value is 2/3. How do we find the fraction?

$\star\:\:\:\bf\large\underline\blue{Solution:-}$

Let the numerator be x and denominator be y.

Therefore, according to the given conditions,

$\sf \frac{x - 1}{y - 1} = \frac{1}{2} \: ...(i)$

And,

$\sf \frac{x + 1}{y + 1} = \frac{2}{3} \: ...(ii)$

From (i),we can write that,

$\sf2(x - 1) = y - 1$

$\sf \implies2x - y = 1 \: ...(iii)$

From (ii), we can write that,

$\sf3(x + 1) = 2(y + 1)$

$\sf \implies3x - 2y = - 1 \: ...(iv)$

Multiplying equation (iii) by 2,we get,

$\sf4x - 2y = 2 \: ...(v)$

Subtracting (iv) from (v), we get,

$\sf4x - 3x = 2 - ( - 1)$

$\sf \implies x = 3$

Now, from equation (iv),

$\sf4x - 2y = 2$

$\sf \implies12 - 2y = 2$

$\sf \implies2y = 10$

$\sf \implies y = 5$

Therefore,

$\sf x = 3 \: and \: y = 5$

$\star\:\:\:\bf\large\underline\blue{Answer:-}$

• The fraction is $\sf \frac{3}{5}$