Question

If we add 5 to the denominator and subtract 5 from the numerator of a fraction, it becomes 1/7. If we subtract 3 from the numerator and add 3 to its denominator, it reduces to . Find the fraction.

Answer 1

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Answer 2

Complete Question:-

If we add 5 to the denominator and subtract 5 from the numerator of a fraction, it becomes 1/7. If we subtract 3 from the numerator and add 3 to its denominator, it reduces to 1/3. Find the fraction.

The Fraction is 7/9.

Given:-

The fraction in the first case = 1/7

The fraction in the second case = 1/3

To Find:-

The Fraction.

Solution:-

We can easily find out the Fraction by following these simple steps.

As

The fraction in the first case = 1/7

The fraction in the second case = 1/3

Let the numerator part of the fraction be x and the denominator part of the fraction be y.

Case 1:-

$\frac{x - 5}{y + 5} = \frac{1}{7}$

$7(x - 5) = 1(y + 5)$

$7x - 35 = y + 5$

$7x - y = 40$

Case 2:-

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

$3(x - 3) = 1(y + 3)$

$3x - 9 = y + 3$

$3x - y = 12$

On solving,

7x - y = 40

3x - y = 12

we get,

4x = 28

x = 28/4

x = 7

By putting the value of x in 3x - y = 12

3*7 - y = 12

21 - 12 = y

y = 9

Hence, the Fraction is 7/9.

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