The sum of two number a and b is 15,


The sum of two number $a$ and $b$ is 15 , and the sum of their reciprocals $\frac{1}{a}$ and $\frac{1}{b}$ is $3 / 10$. Find the numbers $a$ and $b$.


Given that $a$ and $b$ be two numbers in such a way that $b=(15-a)$.

Then according to question


$\frac{(b+a)}{a b}=\frac{3}{10}$

$\frac{(a+b)}{a b}=\frac{3}{10}$

By cross multiplication

$10 a+10 b=3 a b$....(1)

Now putting the value of b in equation (1)

$10 a+10(15-a)=3 a(15-a)$

$3 a^{2}-45 a+150=0$


$3\left(a^{2}-15 a+50\right)=0$

$\left(a^{2}-15 a+50\right)=0$

$a^{2}-10 a-5 a+50=0$










When $a=10$ then;



And when $a=5$ then



Thus, two consecutive number be either $a=5, b=10$ or $a=10, b=5$

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