Shortly after Independence, £1 was equivalent to ₹13.37, so its estimated that $1 must have been worth ₹4.16.
Post-Independence, India adopted a fixed exchange rate system. In 1975 $1 was worth ₹8.39 and by 1990 it had crossed ₹17.01
In 1991, India undertook liberalisation. From fixed it became a more flexible exchange rate system. In 1991 $1 was ₹35; by 2000 it became ₹44.31
In 2008, the year of the Global Financial Crisis, the rupee was around 43.30 to the dollar. By 2015 it had ₹66.79.
By 2020, the rupee further depreciated, crossing the ₹74 mark (₹74.31).
In the 2000s, several global events including the Great Financial Crisis and the Covid-19 pandemic had their impact on the rupee.
Post 2022 the rupee further depreciated crossing the 80 mark. 1$ was worth over ₹81. And as of September 2024, it's over 83 (₹83.56) to the dollar.
Trade balances, inflation, interest rates, geopolitics, and foreign investment are key. Apart from this, high inflation depreciates currency