After a rate hike by the US Fed, the difference between interest rates in US and India shrinks which affects the currency trade negatively. This starts a chain reaction, US rate hike leads to increase in interest rates in India. So when the US Fed increases rates, RBI also has to increase interest rates here in India so that the outflows of funds from the FIIs (Foreign Institutional Investors) can be curtailed to save guard the rupee. Simply put, the hike will widen the gap in interest rates between the two countries.