A class has 20 boys with average score 60 and 30 girls with average score 70. What is the class average?
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The total score is 20 × 60 + 30 × 70 = 3,300.
Dividing by 50 students gives 66.
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The total score is 20 × 60 + 30 × 70 = 3,300.
Dividing by 50 students gives 66.
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The total ratio parts are 7, so one part is 35/7 = 5 liters.
Water is two parts, or 10 liters.
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Thirty percent of 20 liters is 0.30 × 20.
This equals 6 liters.
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The solution contains 4 liters of salt, which remains unchanged.
For salt to be 25%, total volume must be 16 liters, so 6 liters are added.
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For direct variation, x/y is constant.
The constant is 18/6 = 3, so x = 3 × 10 = 30.
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The decrease is Rs. 75.
The percentage decrease is 75/500 × 100 = 15%.
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The greatest common divisor of 24 and 36 is 12.
Dividing both terms by 12 gives 2:3.
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Let the number be x, so 0.40x = 72.
Dividing by 0.40 gives x = 180.
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Percent means per hundred.
Thus, 3.5% = 3.5 ÷ 100 = 0.035.
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The sum of the first n natural numbers is n(n + 1)/2.
For n = 10, the sum is 10 × 11 ÷ 2 = 55.
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The required percentage is 45/250 × 100.
This equals 18%.
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The sum of the first n odd numbers equals n².
For n = 8, the sum is 8² = 64.