Question

The sum of numerator and denominator of a fraction is 10. If the numerator is increased by 1 and the denominator is reduced by 1, the value of fraction becomes 2/3. Find the fraction.


please Its Urgent. ​

Answer 1

Answer:

• The original fraction is 3/7.

Step-by-step explanation:

Given that:

• The sum of numerator and denominator of a fraction is 10.
• If the numerator is increased by 1 and the denominator is decreased by 1, the value of the fraction becomes 2/3.

To Find:

• The original fraction.

Let us assume:

• The numerator be x.

Then,

• The denominator will be (10 - x).

The fraction is,

$\sf{\dasharrow\dfrac{x}{10-x}}$

After increasing and decreasing the numerator and denominator:

• The new numerator = x + 1
• The new denominator = 10 - x - 1 = 9 - x

And, the new fraction is,

$\sf{\dasharrow\dfrac{x+1}{9-x}}$

According to the question:

$\sf{\longmapsto\dfrac{x+1}{9-x}=\dfrac{2}{3}}$

By cross-multiplication,

$\sf{\longmapsto3(x+1)=2(9-x)}$

Opening the brackets,

$\sf{\longmapsto3x+3=18-2x}$

Transposing variables to LHS, constants to RHS and changing their sign,

$\sf{\longmapsto3x+2x=18-3}$

Solving further,

$\sf{\longmapsto5x=15}$

Transposing 5 from LHS to RHS and changing its sign,

$\sf{\longmapsto x=\dfrac{15}{5}}$

Dividing the numbers,

$\sf{\longmapsto x=3}$

Hence,

• Value of x = 3

Therefore,

• The original numerator = x = 3
• The original denominator = (10 - x) = 10 - 3 = 7

And, the original fraction is,

$\bf{\dasharrow \dfrac{3}{7}}$