Let T be the number of 20c coins and F be the number of 50c coins.
T/F=3/7, so T=3F/7.
Now we add 20 coins of each denomination: (T+20)/(F+20)=7/11 the new ratio.
So 11T+220=7F+140, and substituting for T we get: 33F/7+220=7F+140.
Multiply through by 7: 33F+1540=49F+980. F(49-33)=1540-980=560; 16F=560, F=560/16=35.
So T=3*35/7=15.
T/F=15/35=3/7 and 35/55=7/11. So the figures are OK and the initial number of 20c was 15 and of 50c was 35. The initial amount was 15*20+35*50=300+1750=2050c or $20.50.