Question

POLE
18. The numerator of a fraction is four less than its denominator. If 1 is added to both, its
numerator and denominator, the fraction becomes
1
Find the fraction.
2​

Answer 1

Correct Question:

The numerator of a fraction is four less than its denominator. If 1 is added to both, its numerator and denominator, the fraction becomes ½. Find the fraction.

Answer:

The required fraction is 3/7.

Step-by-step explanation:

Given:

• The numerator of a fraction is four less than its denominator.
• If 1 is added to both, its numerator and denominator, the fraction becomes ½.

To find:

The fraction.

Solution:

Let the numerator of a fraction be x and denominator of a fraction be y respectively.

Hence, the fraction is x/y

The numerator of a fraction is four less than its denominator.

• x = y - 4. ...1

According to the problem,

• (x + 1)/(y + 1) = 1/2

Substitute the value of eq1 in the above equation, we get:

• (y - 4 + 1)/(y + 1) = 1/2
• (y - 3)(y + 1) = 1/2
• 2(y - 3) = 1(y + 1)
• 2y - 6 = y + 1
• 2y - y = 1 + 6
• y = 7

∴ The denominator of fraction = 7

Now, find the denominator by substituting the value of y in eq1, we get:

• x = 7 - 4
• x = 3

∴ The numerator of fraction = 3

Hence, the required fraction = Numerator/Denominator = 3/7

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