Work backwards: the amount left after each step is a percentage of the amount before it.

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After buying shoes, $630 remained. This is 75% of the amount before shoes (since 25% was spent on shoes).
• Amount before shoes = $630 ÷ 75 × 100 = $630 ÷ 0.75 = $840
• $840 is 70% of the remainder after the phone (since 30% was spent on the watch).
• Remainder after phone = $840 ÷ 70 × 100 = $840 ÷ 0.7 = $1200
• Original savings = $1200 + $450 = $1650

Mr Tan had $1650 at first.
Check: $1650 − $450 = $1200; 30% of $1200 = $360 (watch); $1200 − $360 = $840; 25% of $840 = $210 (shoes); $840 − $210 = $630. ✓