Solve Average Practice Questions with Answers in Quantitive Aptitude Section for Sarkari Exams. Here you can easily understand and expert the in averages subject. We added from beginners to advanced level Average Problems with Solutions.
Q1. A cyclist covers three different segments of a journey in the ratio 2:3:5. The speeds in these segments are 12 km/h, 18 km/h, and 24 km/h, respectively. Find the average speed for the entire journey.
Correct Answer:
16.2 km/h
Explanation: Distances = $2x$, $3x$, $5x$; Total distance = $10x$.
Total time = $\frac{2x}{12} + \frac{3x}{18} + \frac{5x}{24} = 1.67x$.
Average speed = $\frac{\text{Total distance}}{\text{Total time}} = 16.2 \, \text{km/h}$.
Q2. A, B, and C are partners in a business. Their profits are in the ratio 5:6:9. If the average profit is $50,000, find the total profit.
Correct Answer:
$180,000
Explanation: Average profit = Total profit / 3 = 50,000 / 3
Total profit = 50,000 × 3 = 150,000.
Q3. A school has 80% boys and 20% girls. The average weight of boys is 60 kg, and the average weight of girls is 50 kg. Find the average weight of all students.
Q4. A mixture contains 20% sugar. How much pure sugar should be added to 50 kg of this mixture to make the sugar content 40%?
Correct Answer:
20 kg
Explanation: Sugar in the mixture = $50 \times 0.2 = 10$ kg.
Let $x$ kg of sugar be added. Total sugar = $10 + x$, total weight = $50 + x$.
$\frac{10 + x}{50 + x} = 0.4$. Solving, $x = 20$.
Q5. A student’s marks in four subjects are in the ratio 3:4:5:6. If his overall average is 60, what are his marks in the subject with the highest score?
Correct Answer:
72
Explanation: Let the marks be 3x, 4x, 5x, 6x.
Average = (3x + 4x + 5x + 6x) / 4 = 60.
Solving 18x = 240, x = 4.
Highest marks = 6x = 72.
Q6. In a group of 40 people, 25% are vegetarians, and the rest are non-vegetarians. If the average age of vegetarians is 30 years and the average age of non-vegetarians is 40 years, find the average age of the group.
Q7. A tank contains 100 liters of a 30% alcohol solution. How much pure alcohol must be added to make it a 50% alcohol solution?
Correct Answer:
40 liters
Explanation: Alcohol in solution = $100 \times 0.3 = 30$ liters.
Let $x$ liters of pure alcohol be added. Total alcohol = $30 + x$, total solution = $100 + x$.
$\frac{30 + x}{100 + x} = 0.5$.
Solving, $x = 40$.
Q8. Three numbers are in the ratio 2:3:5. If their average is 60, find the largest number.
Correct Answer:
120
Explanation: Let the numbers be $2x$, $3x$, $5x$.
Average = $\frac{2x + 3x + 5x}{3} = 60$.
Solving $10x = 180$, $x = 18$.
Largest number = $5x = 120$.
Q9. The average of 5 positive integers is 20. The maximum possible value of the smallest integer is:
Correct Answer:
28
Explanation: Total = $5 \times 20 = 100$.
To maximize the smallest integer, the other four integers should be minimized, ideally $1, 1, 1, 1$.
Smallest integer = $100 - 4 = 28$.
Q10. A man walks three stretches of his journey in the ratio 1:2:3 at speeds of 5 km/h, 10 km/h, and 15 km/h, respectively. What is his average speed over the entire journey?
Correct Answer:
8.33 km/h
Explanation: Let the distances be $x$, $2x$, $3x$.
Total distance = $6x$, Total time = $\frac{x}{5} + \frac{2x}{10} + \frac{3x}{15} = \frac{6x}{30} = \frac{6x}{12}$.
Average speed = $\frac{6x}{\frac{6x}{12}} = 8.33 \, \text{km/h}$.
Q11. The average of a group of numbers is 60. If 20% of the numbers are increased by 20 and the rest are decreased by 10, what is the new average?
Correct Answer:
60
Explanation: The increase and decrease in sum cancel out because the weighted average changes evenly. The new average remains unchanged at 60.
Q12. A train travels 240 km at a uniform speed. If the speed had been 10 km/h faster, it would have taken 1 hour less to complete the journey. What is the average speed of the train?
Correct Answer:
50 km/h
Explanation: Let the speed = x.
Time Difference = 240/x - 240/x+10 = 1.
Solving
$\frac{240(x + 10) - 240x}{x(x + 10)} = 1$,
$x = 50$.
Q13. A man has two bags weighing 40 kg and 60 kg. He wants to divide both into equal parts such that the difference in average weights of the parts is minimized. What should the weights of the parts be?
Correct Answer:
50 and 50
Explanation: Minimizing the difference in average weights requires dividing into equal total weights
50
50 each.
Q14. The average of 4 numbers is 45. If the first number is 10% more than the second, the second is 20% more than the third, and the fourth is 25% less than the third, find the third number.
Correct Answer:
40
Explanation: Let the third number be x.
Fourth = 0.75x, second = 1.2x, first = 1.1(1.2x) = 1.32x.
Average = x+0.75x+1.2x+1.32x/4 = 45.
Solving, x = 40.
Q15. In a mixture of 120 liters, the ratio of milk to water is 7:5. How much water should be added to make the ratio 3:4?
Correct Answer:
40 liters
Explanation: Milk = 120 × 7/12 = 70, Water = 120 − 70 = 50.
Adding 𝑥
x, new ratio = 70 : (50 + x) = 3 : 4.
Solving 70/(50 + x) = 3/4, x = 40.