Practice Questions
Concept Explanation
Mixed average problems combine multiple concepts: basic average, addition/removal, replacement, weighted average, and average speed.
Strategy
- Identify the type: marks, age, speed, salary, or combined groups.
- Convert average to total sum first.
- Apply the correct formula for the change described.
- For speed, always use total distance / total time.
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Q1 MediumThe average of 50 numbers is 38. If two numbers, namely 45 and 55, are discarded, the average of the remaining numbers is:ExplanationSum of 50 numbers = 50 × 38 = 1900. After discarding 45 and 55, remaining sum = 1900 − 100 = 1800 over 48 numbers. Average = 1800/48 = 37.5.
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Q2 MediumA family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?ExplanationTotal age = 2 × 67 + 2 × 35 + 3 × 6 = 134 + 70 + 18 = 222 years. Number of members = 7. Average = 222/7 = 31 5/7 years.
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Q3 MediumA grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?ExplanationRequired total for 6 months = 6 × 6500 = 39000. Sum of given 5 months = 6435 + 6927 + 6855 + 7230 + 6562 = 34009. Sixth month sale = 39000 − 34009 = Rs. 4991.
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Q4 MediumThe average of 20 numbers is zero. Of them, at most, how many may be greater than zero?ExplanationSum of the 20 numbers = 0. To maximize how many are positive, make 19 numbers positive and one large negative number that cancels their sum. At most 19 numbers can be greater than zero.
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Q5 MediumIn a mixed aptitude set, the average of 5 numbers is 18. One number is removed and the average becomes 16. The removed number is:ExplanationOld sum = 5 × 18 = 90. New sum = 4 × 16 = 64. Removed number = 90 − 64 = 26.
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Q6 MediumClass A (20 students) has average 55 and Class B (30 students) has average 65. The overall average is:ExplanationOverall average = (20 × 55 + 30 × 65)/50 = (1100 + 1950)/50 = 3050/50 = 61.
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Q7 MediumAverage of 8 numbers is 25. If 30 is replaced by 50, the new average is:ExplanationSum increases by 20. New average = 25 + 20/8 = 25 + 2.5 = 27.5.
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Q8 Medium10 kg of rice at Rs. 40/kg is mixed with 20 kg at Rs. 55/kg. The average price per kg of the mixture is:ExplanationWeighted average = (10 × 40 + 20 × 55)/30 = (400 + 1100)/30 = 1500/30 = Rs. 50 per kg.
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Q9 MediumAfter 9 innings a batsman's average is 38. After the 10th innings the average becomes 40. The 10th innings score is:ExplanationOld sum = 9 × 38 = 342. New sum = 10 × 40 = 400. Tenth score = 400 − 342 = 58.
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Q10 HardThe captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?ExplanationLet the team average be x years. Then 11x − (26 + 29) = 9(x − 1) ⇒ 11x − 55 = 9x − 9 ⇒ 2x = 46 ⇒ x = 23 years.
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Q11 HardThe average of 11 results is 50. If the average of the first 6 results is 49 and that of the last 6 is 52, then the sixth result is:ExplanationSum of 11 = 11 × 50 = 550. Sum of first 6 = 6 × 49 = 294. Sum of last 6 = 6 × 52 = 312. Sixth result (counted twice) = 294 + 312 − 550 = 56.
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Q12 HardA car goes 80 km at 40 km/h and returns 80 km at 80 km/h. The average speed for the round trip is:ExplanationEqual distances: average = 2 × 40 × 80 / (40 + 80) = 6400/120 = 53.333… ≈ 53.33 km/h. Time = 2 + 1 = 3 h for 160 km → 160/3 ≈ 53.33 km/h.
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Q13 HardAverage age of 6 persons is 30 years. One aged 42 leaves and one aged 24 joins. The new average is:ExplanationOld sum = 6 × 30 = 180. New sum = 180 − 42 + 24 = 162. New average = 162/6 = 27 years.
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Q14 HardThree groups of 10, 20 and 30 members have averages 40, 50 and 60 respectively. The combined average is:ExplanationCombined average = (10 × 40 + 20 × 50 + 30 × 60)/60 = (400 + 1000 + 1800)/60 = 3200/60 = 53.333… ≈ 53.33.
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DS1 Easy
What is the overall average of the two classes?
Statement IGroup 1 has 20 members with average 55.
Statement IIGroup 2 has 30 members with average 65.
ExplanationBoth groups are required. Overall average = (1100 + 1950)/50 = 61. -
DS2 Medium
What is the average speed of the journey?
Statement IThe total distance covered is 160 km.
Statement IIThe total time taken is 3 hours.
ExplanationAverage speed = distance/time needs both values. Together: 160/3 ≈ 53.33 km/h.
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DS3 Medium
During a screening round, what is the removed number from the set?
Statement IThe average of 5 numbers is 18.
Statement IIAfter one number is removed, the average of the remaining 4 numbers is 16.
ExplanationTogether: removed = 5 × 18 − 4 × 16 = 90 − 64 = 26. Neither statement alone is sufficient. -
DS4 Hard
In a quantitative interview, is the combined average above 60?
Statement IClass A has 20 students with average 55.
Statement IIClass B has 30 students with average 65.
ExplanationTogether: combined average = 61, which is above 60. Both statements are needed to decide.