Question

The difference between the denominator and the numerator of a fraction is 3. If the denominator as well as the numerator is 4 increased by 4, then fraction becomes 5 Find the original fraction.​

Answer 1

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Answer 2

Given:

The difference between the denominator and the numerator of a fraction is 3. If the denominator, as well as the numerator, is 4 increased by 4, then the fraction becomes 5. Find the original fraction.​

Correct question: The difference between the denominator and the numerator of a fraction is 3. If the denominator, as well as the numerator, is 4 increased by 4, then the fraction becomes 4/5. Find the original fraction.​

To find:

The original fraction

Solution:

The difference between the denominator and the numerator of a fraction is 3, so we can form the equation as,

d - n = 3 . . . (1)

If the denominator, as well as the numerator, is 4 increased by 4, then the fraction becomes 4/5, so we can form the equation as,

$\frac{n \:+\: 4}{d \:+\: 4} = \frac{4}{5}$

$\implies 5n + 20 = 4d + 16$

$\implies 5n - 4d = 16 - 20$

$\implies 5n - 4d = -4$ . . . (2)

On multiplying equation (1) by 5, we get

5d - 5n = 15 . . . (3)

On adding equations (2) and (3), we get

-5n + 5d = 15

5n - 4d = -4

+

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    d = 11 ← denominator

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On substituting the value of d = 11 in equation (1), we get

$11 - n = 3$

$\implies n = 11 - 3$

$\implies n = 8$ ← numerator

Thus, the original fraction is → $\bold{\underline{\frac{8}{11} }}$.

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Also View:

The numerator of a fraction is 3 more than the denominator. If the numerator and the denominator are increased by 5 the fraction becomes 10/7. Find the fraction.

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