Question

Divide 15 into two parts such that sum of their reciprocal will be 3/10

Answer 1

5 and 10
1/5 + 1/10 = 3/10

Answer 2

5 and 10 are the two parts of the number 15, which the sum of reciprocal will be $\frac{3}{10}$.  

To find:

Find the two parts of the number 15, if the reciprocal will be $\frac{3}{10}$.

Solution:

Let one part of the number is x

Therefore, another part of the number is 15-x

According to the question, sum of their reciprocal will be$\frac{3}{10}$.

Therefore,  

$\frac{1}{x}+\frac{1}{(15-x)}=\frac{3}{10}$

$\frac{(15-x)+x}{x(15-x)}=\frac{3}{10}$

$15 \times 10=3 x \times(15-x)$

$1+50=45 x-3 x^{2}$

$x^{2}-15 x+50=0$

$\begin{array}{l}{ x^{2}-10 x-5 x+50=0} \\ {(x-10)(x-5)=0}\end{array}$

x=10; x=5

Hence, the two parts of the number 15 are 10 and 5.