Question

3. The denominator of a fraction is 4 more than the numerator. If 1 is added to the numerator and 2 is

added to the denominator, the value of the fraction becomes. Find the original number.​

Answer 1

Answer:

The denominator of a fraction is 4 more than the numerator. If 1 is added to the numerator and 2 is added to the denominator, the value of the fraction becomes 4/5. Hence, the original fraction = x/y = 19/23.

Step-by-step explanation:

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Answer 2

Correct Question :

• The denominator of a fraction is 4 more than the numerator. If 1 is added to the numerator and 2 is added to the denominator, the value of the fraction becomes 4/5. Find the original number.

Answer :

• Original number is 9/23

To find :

• Original number

Solution :

• Let the numerator be x
• Let the denominator be y

Case - 1 :

According to question, Given that,

The denominator of a fraction 4 more than the numerator then,

》x = y - 4

x = y - 4 is equation (1)

Case - 2 :

And also given that , if 1 is added to the numerator and 2 is added to the denominator The value of the fraction becomes 4/5 then,

》(n + 1) / (d + 2) = 4/5

》(x + 1) / (y + 2) = 4/5

》5(x + 1) = 4(y + 2)

》5x + 5 = 4y + 8

》5x - 4y = 3

5x - 4y = 3 is equation (2)

Now Substituting the value of x equation (1) in equation (2) we get ,

》x = y - 4 + 5x - 4y = 3

》5(y - 4) - 4y = 3

》5y - 20 - 4y = 3

》y = 23

Now Substituting the value of y = 23 in equation (1) we get,

》x = y - 4

》x = 23 - 4

》x = 19

So, x/y

Answer is 19/23

Hence , Original number is 19/3

Verification :

》x = y - 4

》19 = 23 - 4

》19 = 19

And ,

》(19 + 1) / (23 + 2)

》20/25

》4/5

Hence Verified