Question

A fraction become 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to it's denominator. Find the fraction?​

Answer 1

Answer:

The given fraction is 5/12.

Step-by-step explanation:

Given:

• A fraction become 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to it's denominator.

To find:

• The fraction.

Solution:

Let the numerator be x and the denominator be y.

Therefore, the fraction is x/y

According to the problem,

A fraction becomes 1/3 when 1 is subtracted from the numerator.

• (x - 1)/y = 1/3
• 3(x - 1) = y
• y = 3x - 3 ...1

A fraction becomes 1/4 when 8 is added to it's denominator.

• x/(y + 8) = 1/4
• 4x = y + 8
• y = 4x - 8 ...2

On combining eq1 and eq2, we have:

• 3x - 3 = 4x - 8
• 4x - 3x = - 3 + 8
• x = 5

∴ The numerator of a fraction = 5

Now, find the denominator, by substituting the value of x in eq1, we have:

• y = 3 × 5 - 3
• y = 15 - 3
• y = 12

∴ The denominator of a fraction = 12

Hence, The required fraction is 5/12.

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