If Ayana gave 1/5 of the peanuts to her sister and then 3/4 of what remained to another sister, she kept 1/5 for herself. It's because:
5/5 is what she got at the beginning
5/5 - 1/5 = 4/5 is what she gave to one sister
3/4 of what remained is 3/4 * 4/5 = 12/20 = 3/5 for another sister
So now 4/5 - 3/5 = 1/5 is what she kept for herself.