Question

The ratio of the numerator and the denominator of a rational number is 3:4. if 4 is added to the numerator and 6 is subtracted from the denominator, then the rational number becomes 8/5. Then the original rational number is

Answer 1

your answer is2/3=2:3

Answer 2

✺Answer:

♦️GiveN

Ratio of numerator and denominator = 3:4

4 is added to numerator and 6 is subtracted from denominator.

New ratio of numerator and denominator = 8:5

♦️To FinD

Find the original rational number.

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✺Explanation of Q.

The above question is asking about a fraction in which the ratio of numerator to denominator is 3:4, when 4 is added to numerator and 6 is subtracted from denominator, the fraction changes and now the ratio becomes 8:5. So, we have to find the numerator and denominator of original fraction and the original fraction itself.

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✺Concept to be used:

The question can be done using two methods.

Method-1 : By forming a linear equation in one variable and solving it.

Method-2 : By taking 2 variables for numerator and denominator separately and solving it accordingly.

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✺Solution:

According to question,

Ratio of Numerator to Denominator = 3:4

So, let the Numerator and denominator be 3x and 4x

Now, 4 is added to numerator, New Numerator =3x+4

6 is subtracted from denominator, New Denominator = 4x-6

¤ New ratio = 8 : 5

So, this would be,

♠️ Then, Numerator = 3x = 3(4) = 12

And Denominator = 4x =4(4) = 16

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Let the numerator be x and denominator be y

Then,

Now, 4 is added to numerator = x + 4

And 6 is subtracted from denominator = y-6

¤ New ratio = 8:5

Then,

Now, putting equation (1) in equation (2)

♠️ Thus, Numerator is 12

And denominator is 16.

✒Hence, Solved!

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