Cherry gave 1/5 to her daughter, so 4/5 remains. Groceries take 1/4 of remainder, and 2/3 of what is left after groceries goes to savings.

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• Daughter → 1/5 × $1000 = $200
• Remainder → $1000 − $200 = $800
• Groceries → 1/4 × $800 = $200
• After groceries → $800 − $200 = $600
• Saved in bank → 2/3 × $600 = $400

Cherry saved $400 in the bank.
Check: Daughter $200 + Groceries $200 + Saved $400 + Not saved $200 = $1000. ✓