Practice Questions
Concept Explanation
When values have different weights (importance or frequency), use the weighted average:
Weighted average = Σ (weight × value) / Σ weights
Key Idea
- Heavier weights pull the average toward that value.
- If all weights are equal, weighted average equals the simple average.
Example
Test 1: 40 marks, score 70 (weight 3). Test 2: 60 marks, score 80 (weight 2). Weighted average = (3×70 + 2×80)/(3+2) = 74.
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Q1 Easy10 kg of rice at Rs. 20 per kg is mixed with 15 kg of rice at Rs. 30 per kg. The average price of the mixture per kg is:ExplanationWeighted average = (10 × 20 + 15 × 30) / (10 + 15) = (200 + 450) / 25 = 650 / 25 = Rs. 26 per kg.
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Q2 Easy4 apples weigh 60 g each and 6 apples weigh 80 g each. The average weight per apple is:ExplanationTotal weight = (4 × 60) + (6 × 80) = 240 + 480 = 720 g. Average = 720 / 10 = 72 g.
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Q3 EasyThe weighted average of 30 (weight 2) and 45 (weight 3) is:ExplanationWeighted average = (2 × 30 + 3 × 45) / 5 = (60 + 135) / 5 = 195 / 5 = 39.
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Q4 EasyTwo values 25 and 35 have equal weights. Their weighted average is:ExplanationEqual weights reduce weighted average to the simple mean: (25 + 35) / 2 = 30.
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Q5 Easy3 kg of tea at Rs. 40 per kg is mixed with 7 kg at Rs. 60 per kg. The average cost per kg is:ExplanationAverage cost = (3 × 40 + 7 × 60) / 10 = (120 + 420) / 10 = 540 / 10 = Rs. 54.
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Q6 MediumIn the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?ExplanationRuns in first 10 overs = 10 × 3.2 = 32. Runs still needed = 282 − 32 = 250. Required run rate in remaining 40 overs = 250 / 40 = 6.25.
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Q7 MediumA student scores 70 (weight 3) and 80 (weight 2). The weighted average score is:ExplanationWeighted average = (3 × 70 + 2 × 80) / (3 + 2) = (210 + 160) / 5 = 370 / 5 = 74.
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Q8 MediumMaths (4 credits) score 80, English (3 credits) score 70 and Science (3 credits) score 90. The credit-weighted average is:ExplanationWeighted average = (4 × 80 + 3 × 70 + 3 × 90) / (4 + 3 + 3) = (320 + 210 + 270) / 10 = 800 / 10 = 80.
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Q9 Medium20 litres of milk at Rs. 24 per litre is mixed with 30 litres at Rs. 30 per litre. The average price per litre is:ExplanationWeighted average = (20 × 24 + 30 × 30) / 50 = (480 + 900) / 50 = 1380 / 50 = Rs. 27.6.
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Q10 MediumA batsman scored at a run rate of 4 in 15 overs and 6 in the next 25 overs. His overall run rate for 40 overs is:ExplanationTotal runs = (15 × 4) + (25 × 6) = 60 + 150 = 210. Overall run rate = 210 / 40 = 5.25.
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Q11 HardA library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:ExplanationA 30-day month beginning on Sunday has Sundays on days 1, 8, 15, 22 and 29 — that is 5 Sundays and 25 other days. Total visitors = (5 × 510) + (25 × 240) = 2550 + 6000 = 8550. Average per day = 8550 / 30 = 285.
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Q12 HardThe average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ratio of the number of boys to the number of girls in the class is:ExplanationLet the number of boys be b and girls be g. Then (16.4b + 15.4g)/(b + g) = 15.8. Expanding: 16.4b + 15.4g = 15.8b + 15.8g → 0.6b = 0.4g → b/g = 2/3. By allegation: boys : girls = (15.8 − 15.4) : (16.4 − 15.8) = 0.4 : 0.6 = 2 : 3.
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Q13 HardAn alloy is made of 2 parts copper of density 8 and 3 parts zinc of density 6. The average density of the alloy is:ExplanationAverage density = (2 × 8 + 3 × 6) / (2 + 3) = (16 + 18) / 5 = 34 / 5 = 6.8.
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Q14 HardRs. 5,000 is invested at 8% and Rs. 10,000 at 12%. The weighted average rate of interest is:ExplanationWeighted rate = (5000 × 8 + 10000 × 12) / 15000 = (40000 + 120000) / 15000 = 160000 / 15000 = 32/3 ≈ 10.67%.
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DS1 Easy
In a grade-point practice set, what is the weighted average of two scores?
Statement IValue 70 has weight 3 and value 80 has weight 2.
Statement IIThe total of the weights is 5.
ExplanationStatement I already gives both values and both weights, so weighted average = (210 + 160) / 5 = 74. Statement II alone is insufficient. -
DS2 Easy
A retail mixing problem asks for the average price per kg. What is the average price?
Statement I10 kg were bought at Rs. 20 per kg.
Statement II15 kg were bought at Rs. 30 per kg.
ExplanationEach statement alone gives only one lot. Together: average = (200 + 450) / 25 = Rs. 26 per kg.
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DS3 Medium
During a campus drill, is the weighted average greater than 50?
Statement IThe two values are 45 with weight 2 and 55 with weight 3.
Statement IIThe total weight is 5.
ExplanationStatement I: (90 + 165) / 5 = 51, which is greater than 50. Statement II alone does not give the values. -
DS4 Medium
An investment worksheet asks for the weighted average interest rate. What is the rate?
Statement IRs. 5,000 is invested at 8%.
Statement IIRs. 10,000 is invested at 12%.
ExplanationBoth amounts and rates are needed. Together: (40000 + 120000) / 15000 = 10.67% approximately.