Practice Questions
Concept Explanation
When two or more groups are merged, the combined average is:
Combined average = (n₁×A₁ + n₂×A₂) / (n₁ + n₂)
Key Idea
- Find total sum of each group, add them, divide by total count.
- The larger group pulls the combined average toward its own average.
Example
Group 1: 30 students, avg 40. Group 2: 20 students, avg 55. Combined = (1200 + 1100)/50 = 46.
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Q1 EasyGroup 1 has 30 students with average 40 and Group 2 has 20 students with average 55. The combined average is:ExplanationCombined average = (30 × 40 + 20 × 55) / 50 = (1200 + 1100) / 50 = 2300 / 50 = 46.
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Q2 EasyBoys: 20 with average height 160 cm. Girls: 30 with average height 165 cm. Combined average height is:ExplanationCombined average = (20 × 160 + 30 × 165) / 50 = (3200 + 4950) / 50 = 8150 / 50 = 163 cm.
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Q3 EasyTwo equal-sized groups have averages 50 and 60. Their combined average is:ExplanationWhen n₁ = n₂, combined average = (A₁ + A₂) / 2 = (50 + 60) / 2 = 55.
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Q4 EasyBatch 1: 50 students, average 65. Batch 2: 50 students, average 75. Combined average is:ExplanationEqual batches: combined average = (65 + 75) / 2 = 70. Alternatively (50 × 65 + 50 × 75) / 100 = 7000 / 100 = 70.
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Q5 MediumThe average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weight of all the boys in the class.ExplanationCombined average = (n₁A₁ + n₂A₂) / (n₁ + n₂). Total weight = (16 × 50.25) + (8 × 45.15) = 804 + 361.2 = 1165.2 kg. Average of all 24 boys = 1165.2 / 24 = 48.55 kg.
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Q6 MediumThere are two sections A and B of a class consisting of 36 and 44 students respectively. If the average marks of section A is 40 and that of section B is 35, the average marks of the entire class is:ExplanationTotal marks = (36 × 40) + (44 × 35) = 1440 + 1540 = 2980. Combined average = 2980 / (36 + 44) = 2980 / 80 = 37.25.
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Q7 MediumThe average of 20 girls is 42 and the average of 25 boys is 40. The average of the whole class is:ExplanationTotal = (20 × 42) + (25 × 40) = 840 + 1000 = 1840. Combined average = 1840 / 45 = 40.888… ≈ 40.89.
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Q8 MediumThree groups have 10, 15 and 25 members with averages 20, 30 and 40 respectively. The combined average is:ExplanationTotal sum = (10 × 20) + (15 × 30) + (25 × 40) = 200 + 450 + 1000 = 1650. Combined average = 1650 / 50 = 33.
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Q9 MediumClass X has 40 students averaging 72 and Class Y has 60 students averaging 78. The combined average is:ExplanationCombined average = (40 × 72 + 60 × 78) / 100 = (2880 + 4680) / 100 = 7560 / 100 = 75.6.
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Q10 MediumDept A: 15 employees, average salary Rs. 48,000. Dept B: 25 employees, average Rs. 52,000. Combined average salary is:ExplanationCombined average = (15 × 48000 + 25 × 52000) / 40 = (720000 + 1300000) / 40 = 2020000 / 40 = Rs. 50,500.
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Q11 MediumTeam P: 12 members, average 35. Team Q: 18 members, average 45. Combined average is:ExplanationCombined average = (12 × 35 + 18 × 45) / 30 = (420 + 810) / 30 = 1230 / 30 = 41.
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Q12 MediumA group of 10 has average 25 and a group of 40 has average 40. Combined average is:ExplanationCombined average = (10 × 25 + 40 × 40) / 50 = (250 + 1600) / 50 = 1850 / 50 = 37.
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Q13 MediumTwo classes: 30 students average 55 and 50 students average 65. Combined average is:ExplanationCombined average = (30 × 55 + 50 × 65) / 80 = (1650 + 3250) / 80 = 4900 / 80 = 61.25.
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Q14 HardIn a company, 100 employees average Rs. 30,000 and 200 employees average Rs. 36,000. Overall average salary is:ExplanationOverall average = (100 × 30000 + 200 × 36000) / 300 = (3000000 + 7200000) / 300 = 10200000 / 300 = Rs. 34,000.
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DS1 Easy
In a two-section merger drill, what is the combined average of the two groups?
Statement IGroup 1 has 30 students with average 40.
Statement IIGroup 2 has 20 students with average 55.
ExplanationBoth group sizes and averages are required. Together: combined average = (1200 + 1100) / 50 = 46. -
DS2 Easy
An HR analytics sheet asks for the overall average salary of two departments. What is the overall average?
Statement IDepartment A: 15 employees averaging Rs. 48,000.
Statement IIDepartment B: 25 employees averaging Rs. 52,000.
ExplanationNeed both departments. Together: overall average = (720000 + 1300000) / 40 = Rs. 50,500.
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DS3 Medium
For two equal-sized campus batches, what is the combined average?
Statement IThe first batch average is 48.
Statement IIThe second batch average is 52.
ExplanationWith equal sizes, combined average = (A₁ + A₂) / 2. Both averages are needed, so together the answer is (48 + 52) / 2 = 50. -
DS4 Medium
A placement trainer asks whether the combined average is closer to the larger group's average. Is it closer to 50 than to 20?
Statement IGroup 1 has 10 members with average 20.
Statement IIGroup 2 has 90 members with average 50.
ExplanationTogether: combined = (200 + 4500) / 100 = 47, which is closer to 50 than to 20. Each statement alone is insufficient.