Question

If the numerator of a fraction is increased by 1, it becomes 1/3 and if the denominator is increased by 1, the fraction becomes 1/4 What is the fraction ?​

Answer 1

Answer:

12/20

Step-by-step explanation:

is the correct answer

Answer 2

Answer

Let the numerator be a.

Let the denominator be b.

So, the fraction becomes

$\sf \dashrightarrow \dfrac{a}{b}$

According to the first statement,

The numerator is increased by 1.

$\sf \dashrightarrow \dfrac{a + 1}{b} = \dfrac{1}{3}$

$\sf \dashrightarrow 3(a + 1) = b$

$\sf \dashrightarrow 3a + 3 = b$

$\sf \dashrightarrow 3a - b = -3 \: \: --- (i)$

According to second statement,

$\sf \dashrightarrow \dfrac{a}{b + 1} = \dfrac{1}{4}$

$\sf \dashrightarrow 4a = b + 1$

$\sf \dashrightarrow 4a - b = 1 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow 3a - b = -3$

$\sf \dashrightarrow 3a = -3 + b$

$\sf \dashrightarrow a = \dfrac{-3 + b}{3}$

Now, let's find the value of b by second equation.

$\sf \dashrightarrow 4a - b = 1$

$\sf \dashrightarrow 4 \bigg( \dfrac{-3 + b}{3} \bigg) - b = 1$

$\sf \dashrightarrow \dfrac{-12 + 4b}{3} - b = 1$

$\sf \dashrightarrow \dfrac{-12 + 4b - 3b}{3} = 1$

$\sf \dashrightarrow \dfrac{-12 + b}{3} = 1$

$\sf \dashrightarrow -12 + b = 3$

$\sf \dashrightarrow b = 3 + 12$

$\sf \dashrightarrow b = 15$

Now, let's find the value of a by first equation.

$\sf \dashrightarrow 3a - b = -3$

$\sf \dashrightarrow 3a - 15 = -3$

$\sf \dashrightarrow 3a = -3 + 15$

$\sf \dashrightarrow 3a = 12$

$\sf \dashrightarrow a = \dfrac{12}{3}$

$\sf \dashrightarrow a = 4$

We know that, the values of a and b are 15 and 4. So, the fraction becomes

$\sf \dashrightarrow \dfrac{a}{b} = \dfrac{4}{15}$

Hence, the original fraction is 4/15.