Question

The denominator of a fraction is 2 more than numerator. If the numerator as well as denominator is increased by 4, the fraction becomes 8/10. Find the original fraction.

Answer 1

Explanation:

let the numerator be=x

denominator=x+2

fraction=x/x+2

ATQ

x+4/x+2+4=8/10

x+4/x+6=8/10

10(x+4)=8(x+4)

10x+40=8x+48

10x-8x=48-40

2x=8

x=4

Answer 2

The original fraction is 2/3.

Given:

• The denominator of a fraction is 2 more than numerator.

• If the numerator as well as denominator is increased by 4, the fraction becomes 8/10.

To Find:

Find the original fraction.

Solution:

Let's assume the numerator of the original fraction to be x.

According to the problem, the denominator is 2 more than the numerator, so the denominator would be (x+2).

Now, the problem states that if we increase both the numerator and denominator by 4, we get a new fraction, which is equal to 8/10.

So, the new numerator would be (x+4) and the new denominator would be (x+2+4), which simplifies to (x+6).

Therefore, we can write the equation:

(x+4)/(x+6) = 8/10

Cross-multiplying, we get:

10(x+4) = 8(x+6)

Expanding and simplifying, we get:

10x + 40 = 8x + 48

Subtracting 8x from both sides, we get:

2x + 40 = 48

Subtracting 40 from both sides, we get:

2x = 8

Dividing both sides by 2, we get:

x = 4

So,  fraction = x/(x +2) = (4/6) = 2/3.

So the original fraction was x/(x+2), which is 4/6, or simplified to 2/3.


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