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A fraction becomes $13$ when 1 is subtracted from the numerator and it becomes $14$ when 8 is added to its denominator. The fraction is

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\frac{5}{12}

\frac{7}{12}

\frac{3}{4}

\frac{5}{7}

answer is A.

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Detailed Solution

Given that, when 1 is subtracted from the numerator then the fraction becomes

13

.
Let x be the numerator and y be the denominator of the fraction.
Then, the fraction becomes

x y

.
From given,

x − 1 y = 13

⇒ 3 (x − 1) = y ⇒ 3 x − 3 = y ------(i)

Also given that when 8 is added to its denominator then the fraction becomes

14

⇒ x y + 8 = 14

⇒ 4 x = y + 8

----(ii)
On putting the value of y from equation (i) in equation (ii), we get

4 x = y + 8

⇒ 4 x = 3 x − 3 + 8 ⇒ 4 x − 3 x = 5 ⇒ x = 5

For determining the value of y, we put the value of x in equation (i), we get

3 x − 3 = y ⇒ 35 − 3 = y ⇒ 15 − 3 = y ⇒ y = 12

Hence, the required fraction is,

\Rightarrow

\frac{x}{y} = \frac{5}{12} .

Therefore, the correct option is 1.

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