Question

If 4 is added to the numerator of a fraction it becomes 1/3 and if 3 is added to the denominator it becomes 1/6 then find the numerator and denominator is?

Answer 1

Answer:

Numerator is 5 and the denominator is 27

Step-by-step explanation:

Let the fraction be $\frac{x}{y}$

So, by the problem,

$\frac{x + 4}{y} = \frac{1}{3}$

or, 3(x + 4) = y

or, 3x + 12 = y

or,  3x - y  = -12  equation (1)

Now,

$\frac{x}{y+3} = \frac{1}{6}$

or, y+3 = 6x

or, 6x - y = 3 equation (2)

From equation (1) and (2) we get,

3x - y = -12

6x - y = 3

-    +     -

------------------------

3x - 6x = -12 - 3

or, -3x = -15

or, 3x = 15

or, x = $\frac{15}{3}$

or, x = 5

Putting the value of x in equation 2 we get,

6x - y = 3

or, 6 * 5 - y = 3

or, 30 - y = 3

or, - y = 3 - 30

or, - y = -27

or, y = 27

The numerator is 5 and the denominator is 27

Answer 2

Answer:  $\frac{5}{27}$

Step-by-step explanation:

• Let the fraction be $\frac{x}{y}$.
• According to question, $\frac{x+4}{y} =\frac{1}{3}$

                                           ⇒ 3(x+4)=y

                                           ⇒3x+12=y

                                           ⇒ 3x-y= -12     eq(1)

And,$\frac{x}{y+3}=\frac{1}{6}$

    ⇒ 6x=y+3

    ⇒ 6x-y=3        eq(2)

• Now, eq(2) - eq(1)

        6x-y-3x+y=3+12

    ⇒ 3x=15

    ⇒ x=$\frac{15}{3}$

    ∴ x=5

and y=27.

• Hence, the required fraction is $\frac{5}{27}$.

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