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The sum of two number is 15 ,if the sum of reciprocal is 3/10 find the no

Posted by Naresh Krish 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

Let the numbers be x and 15 - x.

According to question,
{tex}\frac { 1 } { x } + \frac { 1 } { 15 - x } = \frac { 3 } { 10 }{/tex}
{tex}\Rightarrow \quad \frac { 15 - x + x } { x ( 15 - x ) } = \frac { 3 } { 10 }{/tex}
{tex}\Rightarrow \quad \frac { 15 } { x ( 15 - x ) } = \frac { 3 } { 10 }{/tex}

Cross multiply,
{tex}\Rightarrow{/tex}{tex}150=3x(15-x){/tex}
{tex}\Rightarrow{/tex} {tex}150=45x-3x^2{/tex}

^{{tex}\Rightarrow 150=3(15x-x^2){/tex}}
{tex}\Rightarrow{/tex} x² - 15x + 50 = 0
{tex}\Rightarrow{/tex} x² - 10x - 5x + 50 = 0
{tex}\Rightarrow{/tex} x(x - 10) - 5(x -10) = 0
{tex}\Rightarrow{/tex} (x - 10)(x - 5) = 0
{tex}\Rightarrow{/tex} x - 10 = 0 or, x - 5 = 0 {tex}\Rightarrow{/tex} x = 10 or, x = 5
Therefore, numbers are 10 and 5

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