Profit and loss question. A person bought two bicycles for Rs.1600 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the seconds at 10% profit .He would get Rs.5 more.The difference of the cost price of the bicycle was? Here I have some doubts like if cp of 2 cycle is same .if we alter the profit percent then the sp will remain same,and here I am getting confused .Please suggest me.Thank you in advance.Here I didn't get the proper tag to post

Let $x$ and $y$ be the _purchase prices_ of the two bicycles respectively. The profit in the first case then is

$p_1=(1.1-1)x+(1.2-1)y=0.1x+0.2y$

$1.1x$ and $1.2y$ are the _selling prices_.

The profit in the second case is

$p_2=(1.2-1)x+(1.1-1)y=0.2x+0.1y$

$p_2$ is $RS \ 5$ greater than $p_1$. Therefore $p_2=p_1+5$. It follows

$0.2x+0.1y=0.1x+0.2y+5 \quad (1)$

And the sum of x and y is 1600:

$x+y=1600 \quad (2)$

By using (1) and (2) you can calculate $x$ and $y$.