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Answer:
To find the rate, base and percentage use the following formula:
1.) Rate: 60% Base: 55 Percentage: ?
[tex] \sf \: Percentage = Rate × Base \\ \\ \sf \: Percentage = 60 \% \times 55 \\ \\ \sf \: Percentage = 0.6 × 55 \\ \\ \sf \: \tiny{3} \: \: \: \: \\ \tiny{3} \: \: \: \\ \sf \: 0 . 6 \\ \sf \: \underline{\times \: \: 5 \: 5} \: \: \: \: \: \\ \sf \: 3 \: 0 \\ \sf \: \underline{+ \: \: 3 \: 0 \: 0} \: \: \: \: \: \: \: \: \\ \: \: \: \sf \: 3 \: 3.0 \: \: \: \: \: \: [/tex]
Therefore, the percentage is 33
2.) Rate: 20% Base: 75 Percentage: ?
[tex]\sf \: Percentage = Rate × Base \\ \\ \sf \: Percentage = 20 \% \times 75 \\ \\ \sf \: Percentage = 0.2 × 75 \\ \\ \sf \: \sf \: \tiny{1} \: \: \: \: \\ \tiny{1} \: \: \: \\ \sf \: 0 . 2 \\ \sf \: \underline{\times \: \: 7 \: 5} \: \: \: \: \: \\ \sf \: 1 \: 0 \\ \sf \: \underline{+ \: \: 1 \: 4 \: 0} \: \: \: \: \: \: \: \: \\ \: \: \: \sf \: 1 \: 5.0\: \: \: \: \: \: [/tex]
Therefore, the percentage is 15
3.) Rate: 25% Base: ? Percentage: 100
[tex] \sf \: Base = Percentage ÷ Rate \\ \\ \sf \: Base = 100 ÷ 25 \% \\ \\ \sf \: Base = 100 ÷ 0.25 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: 4 \: 0 \: 0 \\ \sf \: 0.2 \: 5 \: | \: \overline{1 \: 0 \: 0 \: 0 \: 0} \\ \sf \: \: \underline{- \: 1 \: 0 \: 0} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: 0 \: 0 \: 0[/tex]
Therefore, the base is 400
4.) Rate: ? Base: 54 Percentage: 27
[tex] \sf \: Rate = Percentage ÷ Base \\ \\ \sf \: Rate = 27 \div 54 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 0.5 \: \: \: \\ \sf \: 5 \: 4 \: | \sf \: \overline{2 \: 7 \: \: \: } \\ \: \: \: \: \: \: \: \: \: \: \: \sf \: 2 \: 7 \: 0 \: \: \: \\ \sf \: \: \: \: \: \: \: \: \underline{ - \: 2 \: 7 \: 0} \: \: \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: 0 \\ \\ \sf \: Rate = 0.5 \\ \\ \sf \: Rate = 50 \%[/tex]
Therefore, the rate is 50%
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