In the FX market, an American bank gives the following quotes:

USD$/$EUR: $1\mathrm{.}20001\mathrm{.}2050$

USD$/$GBP: $1\mathrm{.}79501\mathrm{.}8000$

A British bank gives the following quote:

EUR$/$GBP: $1\mathrm{.}50501\mathrm{.}5070$

How would you execute a set of trades to earn an arbitrage profit assuming there are no transaction costs?

My answer is:

USD $->$ EUR $->$ GBP $->$ USD

i$)$ Buy EUR at ask rate $1\mathrm{.}2050$

ii$)$ Buy GBP at bid rate $1\mathrm{.}5070$

iii$)$ Buy USD at bid rate $1\mathrm{.}7950$

$1\mathrm{.}2050$ USD $->1$ EUR $->0\mathrm{.}6645$ GBP $->1\mathrm{.}1927$ USD

Less amount left than what we started with, so no arbitrage opportunity. I don't know what is wrong with this solution, please let me know!