Question

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Answer 1

Answer:

(7/15)

Step-by-step explanation:

Let the fraction be (x/y).

(i) A fraction becomes (1/3) when 2 is subtracted from the numerator.

⇒ (x - 2)/y = 1/3

⇒ 3x - 6 = y

⇒ 3x - y = 6

(ii) It becomes (1/2) when 1 is subtracted from the denominator.

⇒ x/(y - 1) = 1/2

⇒ 2x = y - 1

⇒ 2x - y = -1

On solving (i) * 2 & (ii) * 3, we get

⇒ 6x - 2y = 12

⇒ 6x - 3y = -3

   -----------------

        y = 15

Substitute y = 15 in (i), we get

⇒ 3x - y = 6

⇒ 3x - 15 = 6

⇒ 3x = 21

⇒ x = 7.

Therefore, the fraction is (7/15).

Hope it helps!

Answer 2

$\mathtt{Let\;the\;Fraction\;be : \dfrac{A}{B}}$

$\heartsuit\;\;\mathtt{Fraction\;becomes\;\dfrac{1}{3}\;when\;2\;is\;subtracted\;from\;the\;numerator}$

$\mathtt{\implies \dfrac{A - 2}{B} = \dfrac{1}{3}}$

$\mathtt{\implies 3(A - 2) = B}$

$\mathtt{\implies 3A - 6 = B}$

$\mathtt{\implies 3A - B = 6\;----\;(1)}$

$\heartsuit\;\;\mathtt{Fraction\;becomes\;\dfrac{1}{2}\;when\;1\;is\;subtracted\;from\;the\;denominator}$

$\mathtt{\implies \dfrac{A}{B - 1} = \dfrac{1}{2}}$

$\mathtt{\implies (B - 1) = 2A}$

$\mathtt{\implies B - 2A = 1\;----\;(2)}$

$\texttt{Adding Equations (1) and (2)}$

$\mathtt{\implies 3A - B + B - 2A = 6 + 1}$

$\mathtt{\implies A = 7}$

$\texttt{Substituting Value of A in Equation (1)}$

$\mathtt{\implies 3(7) - B = 6}$

$\mathtt{\implies B = 21 - 6}$

$\mathtt{\implies B = 15}$

$\mathtt{\implies\;The\;Fraction\;is\;\dfrac{7}{15}}$