By selling an article for Rs. 550, a profit of $10\%$  is made then its cost price is

Let C.P $=\text{Rs}.100$

Profit $=10\%$  of 100

$=\text{Rs}.100$

$\therefore \text{S}\text{.P}=\text{110}$

When S.P $=\text{Rs}\text{.110, C}\text{.P}=\text{Rs}.100$

When $\text{S}\text{.P}=\text{Rs}\text{. 550,}\text{C}\text{.P}=\frac{100}{100}\times 550$

$=\text{Rs}\text{.}\text{500}$