Question

Three times the denominator of a fraction is 6 more
than the numerator. The fraction formed when the
denominator is increased by 5 is 5/4. Find the fraction​

Answer 1

Answer:

The fraction is:

$\frac{15}{7}$

Step-by-step explanation:

Let the fraction be:

$\frac{x}{y}$

Now, given that, 3y = x+6

$\frac{3y - 6}{y}$

$\frac{3y - 6}{y + 5} = \frac{5}{4}$

Cross-multiplying and equating to y, we get:

$y = 7$

Then we can find x

$x = 15$

Answer 2

The fraction is $\bf \frac{15}{7}$.

Given:

• Three times the denominator of a fraction is 6 more than the numerator.
• The fraction formed when the denominator is increased by 5 is 5/4.

To find:

• Find the fraction.

Solution:

Step 1:

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

ATQ,

$3y = x + 6$

$\bf - x + 3y = 6...eq1$

$\frac{x}{y + 5} = \frac{5}{4}$

$4x = 5y + 25$

$\bf 4x - 5y = 25...eq2$

Step 2:

Solve equation 1 and 2.

Multiply eq1 by 4 and add both.

$- 4x + 12y = 24 \\ 4x - 5y = 25 \\ - - - - - - - \\ 7y = 49$

$y = \frac{49}{7}$

$\bf y = 7$

Put the value of y in eq1.

$- x + 3 \times 7 = 6$

$- x = 6 - 21$

$\bf x = 15$

Thus,

The fraction is $\bf \frac{15}{7}$.

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