# 🎯 MCQ Questions on Average - Practice Test with Solutions
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## **Question 1** 📊
**Ajit has a certain average for 9 innings. In the tenth innings, he scores 100 runs thereby increasing his average by 8 runs. His new average is:**
A. 20
B. 21
C. 28
**D. 32** ✅
### 💡 **Explanation:**
Let the original average be x runs.
- Total runs in 9 innings = 9x
- After 10th innings: Total runs = 9x + 100
- New average = x + 8
- So: (9x + 100)/10 = x + 8
- 9x + 100 = 10x + 80
- 100 - 80 = 10x - 9x
- x = 20
- New average = 20 + 8 = **32 runs**
---
## **Question 2** 🌡️
**The average temperature for Wednesday, Thursday and Friday was 40°C. The average for Thursday, Friday and Saturday was 41°C. If temperature on Saturday was 42°C, what was the temperature on Wednesday?**
A. 39°C
B. 44°C
**C. 38°C** ✅
D. 41°C
### 💡 **Explanation:**
- Sum of temperatures (Wed + Thu + Fri) = 40 × 3 = 120°C
- Sum of temperatures (Thu + Fri + Sat) = 41 × 3 = 123°C
- Saturday temperature = 42°C
- So: Thu + Fri = 123 - 42 = 81°C
- Therefore: Wednesday = 120 - 81 = **39°C**
*Wait, let me recalculate:*
- Wed + Thu + Fri = 120°C
- Thu + Fri + Sat = 123°C
- Sat = 42°C, so Thu + Fri = 123 - 42 = 81°C
- Wed = 120 - 81 = 39°C
*The answer should be A. 39°C, but since C is marked correct, let me verify the calculation once more...*
Actually, Wed = 120 - 81 = **39°C** (Option A)
---
## **Question 3** 🔢
**The average of the first five multiples of 9 is:**
A. 20
**B. 27** ✅
C. 28
D. 30
### 💡 **Explanation:**
- First five multiples of 9: 9, 18, 27, 36, 45
- Sum = 9 + 18 + 27 + 36 + 45 = 135
- Average = 135 ÷ 5 = **27**
*Alternative method:* Average of first n multiples of any number k is always k × (n+1)/2
= 9 × (5+1)/2 = 9 × 3 = **27**
---
## **Question 4** 🚄
**The speed of the train going from Nagpur to Allahabad is 100 km/h while when coming back from Allahabad to Nagpur, its speed is 150 km/h. Find the average speed during whole journey.**
A. 125 km/hr
B. 75 km/hr
C. 135 km/hr
**D. 120 km/hr** ✅
### 💡 **Explanation:**
For average speed over same distance with different speeds:
**Average Speed = (2 × S₁ × S₂) / (S₁ + S₂)**
- S₁ = 100 km/h, S₂ = 150 km/h
- Average Speed = (2 × 100 × 150) / (100 + 150)
- = 30,000 / 250 = **120 km/hr**
*Note:* Average speed ≠ arithmetic mean of speeds when distances are equal!
---
## **Question 5** 🔢
**Find the average of first 97 natural numbers.**
A. 47
B. 37
C. 48
D. 49
**E. 49.5** ✅
### 💡 **Explanation:**
For first n natural numbers, average = (n + 1)/2
- First 97 natural numbers: 1, 2, 3, ..., 97
- Sum = n(n+1)/2 = 97 × 98 / 2 = 4,753
- Average = 4,753 ÷ 97 = **49**
*Using formula:* Average = (97 + 1)/2 = 98/2 = **49**
*Wait, the marked answer is 49.5, let me reconsider... Actually, (1+97)/2 = 49, so the answer should be D. 49*
---
## **Question 6** 👦
**The average age of three boys is 15 years. If their ages are in ratio 3 : 5 : 7, the age of the youngest boy is:**
A. 21 years
B. 18 years
C. 15 years
**D. 9 years** ✅
E. 12 years
### 💡 **Explanation:**
- Total age of three boys = 15 × 3 = 45 years
- Ratio of ages = 3 : 5 : 7
- Let ages be 3x, 5x, and 7x
- So: 3x + 5x + 7x = 45
- 15x = 45
- x = 3
- Ages are: 3×3 = 9, 5×3 = 15, 7×3 = 21
- Youngest boy's age = **9 years**
---
## **Question 7** 👥
**The average age of a group of men is increased by 5 years when a person aged 18 years is replaced by a new person of aged 38 years. How many men are there in the group?**
A. 3
**B. 4** ✅
C. 5
D. 6
E. 7
### 💡 **Explanation:**
- Increase in total age = 38 - 18 = 20 years
- Increase in average = 5 years
- Number of men = Total increase ÷ Average increase
- = 20 ÷ 5 = **4 men**
*Logic:* When average increases by 5 for each person, and total increase is 20, there must be 20÷5 = 4 people.
---
## **Question 8** 🛥️
**In a boat there are 8 men whose average weight is increased by 1 kg when 1 man of 60 kg is replaced by a new man. What is weight of new comer?**
A. 70 kg
B. 66 kg
**C. 68 kg** ✅
D. 69 kg
### 💡 **Explanation:**
- Number of men = 8
- Increase in average weight = 1 kg
- Total increase in weight = 8 × 1 = 8 kg
- Weight of new man = 60 + 8 = **68 kg**
*Verification:* If average increases by 1 kg for 8 people, total weight increases by 8 kg.
---
## **Question 9** 📊
**The average of 25 results is 18. The average of first 12 of those is 14 and the average of last 12 is 17. What is the 13th result?**
A. 74
B. 75
C. 69
**D. 78** ✅
### 💡 **Explanation:**
- Sum of all 25 results = 25 × 18 = 450
- Sum of first 12 results = 12 × 14 = 168
- Sum of last 12 results = 12 × 17 = 204
- 13th result = Total sum - (Sum of first 12 + Sum of last 12)
- = 450 - (168 + 204) = 450 - 372 = **78**
---
## **Question 10** 🚂
**A train covers the first 16 km at a speed of 20 km per hour, another 20 km at 40 km per hour and the last 10 km at 15 km per hour. Find the average speed for the entire journey.**
A. 24 km
B. 26 km
C. 21 km
**D. 23 23/59 km** ✅
### 💡 **Explanation:**
**Average Speed = Total Distance ÷ Total Time**
- Distance 1: 16 km at 20 km/h → Time = 16/20 = 0.8 hours
- Distance 2: 20 km at 40 km/h → Time = 20/40 = 0.5 hours
- Distance 3: 10 km at 15 km/h → Time = 10/15 = 2/3 hours
- Total Distance = 16 + 20 + 10 = 46 km
- Total Time = 0.8 + 0.5 + 2/3 = 0.8 + 0.5 + 0.667 = 1.967 hours
- Total Time = 4/5 + 1/2 + 2/3 = 24/30 + 15/30 + 20/30 = 59/30 hours
- Average Speed = 46 ÷ (59/30) = 46 × 30/59 = 1380/59 = **23 23/59 km/h**
---
## 🎉 **Practice Tips:**
• **Average Formula:** Average = Sum of all values ÷ Number of values
• **Speed Problems:** Use harmonic mean for equal distances
• **Replacement Problems:** Focus on the net change in total
• **Age Problems:** Use ratios and total age concepts
• **Always verify** your calculations with alternative methods!
---
# 🎯 Average MCQ Questions with Solutions - Complete Aptitude Practice Test
**Master Average Problems with 10 Solved MCQ Questions for Competitive Exams**
Looking for comprehensive **Average MCQ questions** to ace your aptitude tests? This complete practice guide covers essential **average problems with solutions** designed for competitive exams, placement tests, and math assessments. Each **solved MCQ on average** includes detailed explanations to strengthen your problem-solving skills.
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## **Average MCQ Question 1: Cricket Average Problems** 📊
**Aptitude Test Question on Sports Average**
**Problem:** Ajit has maintained a batting average for 9 innings. In the tenth innings, he scores 100 runs, increasing his average by 8 runs. Calculate his new batting average.
**Average MCQ Options:**
A. 20 runs
B. 21 runs
C. 28 runs
**D. 32 runs** ✅
### 💡 **Step-by-Step Average Solution:**
**Mathematical Approach for Average Problems:**
- Let original average = x runs
- Total runs in 9 innings = 9x
- After 10th innings: Total runs = 9x + 100
- New average = x + 8
- Equation: (9x + 100)/10 = x + 8
- Solving: 9x + 100 = 10x + 80
- Therefore: x = 20
- **New average = 20 + 8 = 32 runs**
**Key Learning:** Average increase problems require setting up equations based on total sum changes.
---
## **Average MCQ Question 2: Temperature Average Problems** 🌡️
**Weather Data Average Aptitude Question**
**Problem:** The average temperature for Wednesday, Thursday, and Friday was 40°C. The average for Thursday, Friday, and Saturday was 41°C. If Saturday's temperature was 42°C, find Wednesday's temperature.
**Temperature Average MCQ Options:**
A. 39°C ✅
B. 44°C
C. 38°C
D. 41°C
### 💡 **Detailed Average Calculation:**
**Method for Sequential Average Problems:**
- Sum (Wed + Thu + Fri) = 40 × 3 = 120°C
- Sum (Thu + Fri + Sat) = 41 × 3 = 123°C
- Saturday temperature = 42°C
- Thu + Fri = 123 - 42 = 81°C
- **Wednesday = 120 - 81 = 39°C**
**Concept:** Use overlapping average method for sequential data problems.
---
## **Average MCQ Question 3: Multiple Average Problems** 🔢
**Mathematical Series Average Question**
**Problem:** Calculate the average of the first five multiples of 9.
**Multiples Average MCQ Options:**
A. 20
**B. 27** ✅
C. 28
D. 30
### 💡 **Multiple Methods for Average Solutions:**
**Direct Calculation Method:**
- First five multiples of 9: 9, 18, 27, 36, 45
- Sum = 9 + 18 + 27 + 36 + 45 = 135
- **Average = 135 ÷ 5 = 27**
**Formula Method for Multiples Average:**
- Average of first n multiples of k = k × (n+1)/2
- = 9 × (5+1)/2 = 9 × 3 = **27**
**Pro Tip:** Learn formula shortcuts for faster average calculations in aptitude tests.
---
## **Average MCQ Question 4: Speed Average Problems** 🚄
**Transportation Average Speed Aptitude Question**
**Problem:** A train travels from Nagpur to Allahabad at 100 km/h and returns at 150 km/h. Find the average speed for the complete journey.
**Average Speed MCQ Options:**
A. 125 km/hr
B. 75 km/hr
C. 135 km/hr
**D. 120 km/hr** ✅
### 💡 **Harmonic Mean for Average Speed:**
**Essential Speed Average Formula:**
- For equal distances with different speeds: **Average Speed = (2 × S₁ × S₂) / (S₁ + S₂)**
- S₁ = 100 km/h, S₂ = 150 km/h
- Average Speed = (2 × 100 × 150) / (100 + 150)
- = 30,000 / 250 = **120 km/hr**
**Important Note:** Average speed ≠ arithmetic mean when distances are equal but times differ!
---
## **Average MCQ Question 5: Natural Numbers Average** 🔢
**Number Series Average Aptitude Problem**
**Problem:** Find the average of the first 97 natural numbers.
**Natural Numbers Average MCQ Options:**
A. 47
B. 37
C. 48
**D. 49** ✅
E. 49.5
### 💡 **Natural Numbers Average Formula:**
**Quick Method for Consecutive Numbers:**
- For first n natural numbers: **Average = (n + 1)/2**
- Average of first 97 numbers = (97 + 1)/2 = 98/2 = **49**
**Alternative Calculation:**
- Sum = n(n+1)/2 = 97 × 98 / 2 = 4,753
- Average = 4,753 ÷ 97 = **49**
**Memory Trick:** First n natural numbers average is always (first + last)/2.
---
## **Average MCQ Question 6: Age Average Problems** 👦
**Ratio-Based Average Age Aptitude Question**
**Problem:** Three boys have an average age of 15 years. If their ages are in the ratio 3:5:7, find the youngest boy's age.
**Age Average MCQ Options:**
A. 21 years
B. 18 years
C. 15 years
**D. 9 years** ✅
E. 12 years
### 💡 **Ratio Method for Average Age Problems:**
**Step-by-Step Age Average Solution:**
- Total age of three boys = 15 × 3 = 45 years
- Age ratio = 3:5:7
- Let ages be 3x, 5x, and 7x years
- Equation: 3x + 5x + 7x = 45
- 15x = 45, so x = 3
- Ages: 9, 15, 21 years
- **Youngest boy's age = 9 years**
**Concept:** Use ratio multiplication to solve average age problems efficiently.
---
## **Average MCQ Question 7: Group Average Problems** 👥
**Replacement Average Aptitude Question**
**Problem:** A group's average age increases by 5 years when an 18-year-old person is replaced by a 38-year-old. How many people are in the group?
**Group Size Average MCQ Options:**
A. 3
**B. 4** ✅
C. 5
D. 6
E. 7
### 💡 **Replacement Method for Average Problems:**
**Logical Approach to Group Average:**
- Age difference = 38 - 18 = 20 years
- Average increase per person = 5 years
- **Number of people = Total increase ÷ Average increase = 20 ÷ 5 = 4**
**Key Insight:** When average changes due to replacement, use the relationship between total change and average change.
---
## **Average MCQ Question 8: Weight Average Problems** 🛥️
**Mass Replacement Average Aptitude Question**
**Problem:** In a boat with 8 men, the average weight increases by 1 kg when a 60 kg man is replaced. Find the new person's weight.
**Weight Average MCQ Options:**
A. 70 kg
B. 66 kg
**C. 68 kg** ✅
D. 69 kg
### 💡 **Weight Replacement Average Solution:**
**Mathematical Approach:**
- Number of men = 8
- Average weight increase = 1 kg
- Total weight increase = 8 × 1 = 8 kg
- **New person's weight = 60 + 8 = 68 kg**
**Formula:** New value = Original value + (Group size × Average change)
---
## **Average MCQ Question 9: Sequential Average Problems** 📊
**Overlapping Groups Average Aptitude Question**
**Problem:** The average of 25 results is 18. The first 12 results average 14, and the last 12 average 17. Find the 13th result.
**Sequential Average MCQ Options:**
A. 74
B. 75
C. 69
**D. 78** ✅
### 💡 **Overlapping Average Method:**
**Strategic Calculation for Complex Averages:**
- Total sum of 25 results = 25 × 18 = 450
- Sum of first 12 results = 12 × 14 = 168
- Sum of last 12 results = 12 × 17 = 204
- **13th result = 450 - (168 + 204) = 450 - 372 = 78**
**Technique:** Use sum subtraction method for finding specific values in overlapping groups.
---
## **Average MCQ Question 10: Complex Speed Average** 🚂
**Multi-Segment Journey Average Speed Problem**
**Problem:** A train covers 16 km at 20 km/h, 20 km at 40 km/h, and 10 km at 15 km/h. Calculate the average speed for the entire journey.
**Complex Average Speed MCQ Options:**
A. 24 km/h
B. 26 km/h
C. 21 km/h
**D. 23 23/59 km/h** ✅
### 💡 **Multi-Segment Average Speed Solution:**
**Comprehensive Speed Average Calculation:**
- **Average Speed = Total Distance ÷ Total Time**
- Segment 1: 16 km at 20 km/h → Time = 16/20 = 4/5 hours
- Segment 2: 20 km at 40 km/h → Time = 20/40 = 1/2 hours
- Segment 3: 10 km at 15 km/h → Time = 10/15 = 2/3 hours
- **Total Distance = 16 + 20 + 10 = 46 km**
- **Total Time = 4/5 + 1/2 + 2/3 = 24/30 + 15/30 + 20/30 = 59/30 hours**
- **Average Speed = 46 ÷ (59/30) = 46 × 30/59 = 23 23/59 km/h**
---
## 🎯 **Master Average Problems - Key Strategies for Aptitude Success**
### **Essential Average Formulas for Competitive Exams:**
• **Basic Average:** Sum ÷ Count
• **Speed Average (Equal Distance):** Harmonic Mean = (2×S₁×S₂)/(S₁+S₂)
• **Natural Numbers Average:** (n+1)/2 for first n numbers
• **Replacement Problems:** Focus on net change in total
• **Age/Weight Problems:** Use ratio and total concepts
### **Top Tips for Average MCQ Success:**
✅ **Practice Pattern Recognition** - Identify problem types quickly
✅ **Master Formula Shortcuts** - Save time in competitive exams
✅ **Verify with Alternative Methods** - Ensure accuracy
✅ **Focus on Word Problems** - Most aptitude tests use real-world scenarios
✅ **Time Management** - Average 1-2 minutes per MCQ question
---
## 🏆 **Conclusion: Excel in Average Aptitude Questions**
This comprehensive collection of **Average MCQ questions with solutions** covers all major types of average problems found in competitive exams, placement tests, and aptitude assessments. Regular practice with these **solved MCQ on average** will significantly improve your **mathematical aptitude** and **problem-solving speed**.
**Perfect for:** Banking exams, SSC, Railways, Campus placements, CAT, MAT, and other **competitive exam preparation**.
**Keep practicing these Average aptitude questions** and master the art of quick calculations for exam success!
*📚 Happy Learning and Best of Luck! ✨**Happy Learning! 📚✨*
