This question concerns the mechanism of a reserve currency standard. Two countries, X and Y, have two currencies, x and y, fixed to the reserve currency, the U.S. dollar. Suppose the exchange rate between x and the U.S. dollar is 3x per dollar

Suppose the exchange rate between y and the U.S. dollar is 5y per dollar. Explain (using numbers) the mechanism if the x-y exchange rate was 0.5 x per y.

At this exchange rate, an investor can make an arbitrage profit by selling $100 to the central bank of X (receiving 300 x), then selling your 300 x to the foreign exchange market for 300 x/(0.5 x per y) = 600 y, then buying U.S. dollars in the amount of $120 from the central bank of Y. Thus the foreign exchange market will bid the x-y exchange rate up to 0.6 x per y.