The sum of numerator abd denominator …
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Sia ? 6 years, 4 months ago
Let the numerator and denominator of fraction be x and y respectively.
Then, the fraction is {tex}\frac xy{/tex}.
As per first condition
The sum of the numerator and denominator of a fraction is 4 more than twice the numerator.
x + y = 2x + 4
{tex}\Rightarrow{/tex} -x + y = 4........(i)
According to the second condition,
If the numerator and denominator are increased by 3, they are in the ratio 2 : 3.
{tex}\frac { x + 3 } { y + 3 } = \frac { 2 } { 3 }{/tex}
{tex}\Rightarrow{/tex} 3x + 9 = 2y + 6
{tex}\Rightarrow{/tex}3x - 2y = -3.......(ii)
Multiply (i) by -2, we get
-2x + 2y = 8 ......... (iii)
Adding (ii) and (iii) , we get
and 3x - 2x = -3 + 8
{tex}\Rightarrow{/tex} x = 5
Substituting x = 5 in (i), we get
5 - y = 4
y = 9
Hence, the required fraction is {tex}\frac{5}{9}{/tex}
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