Class 9 Maths Ganita Manjari Chapter 10 MCQs – How Quantities Combine: Understanding Data – for session 2026-27 exam preparation and revision. Before combining two averages, check how many observations each one represents. Before comparing two percentages, check their totals. These habits are central to Class 9 Maths Ganita Manjari Chapter 10 How Quantities Combine: Understanding Data. This set of MCQs puts them into practice through questions on group averages, mixtures, weighted scores, ratings and stacked bar charts. Each answer includes a clear explanation to help you understand the calculation and judge which conclusions the data actually supports.
Class 9 Maths Ganita Manjari Chapter 10 MCQs Set 1
Q1. Two groups have mean values a and b and contain n and m observations, respectively. Which expression gives the mean of all the observations together?
[A]. (a + b)/2
[B]. (an + bm)/(n + m)
[C]. (an + bm)/2
[D]. (a + b)/(n + m)
Q2. Section A has 30 students with an average test score of 70. Section B has 20 students with an average score of 80. What is the combined average score?
[A]. 76
[B]. 75
[C]. 150
[D]. 74
Q3. Three groups each contain 10 observations. Their means are 12, 15 and 18. What is the mean of the combined data?
[A]. 16
[B]. 10
[C]. 15
[D]. 45
Q4. Eight trainees have mean height 165 cm, while two other trainees have mean height 150 cm. Which statement about the combined mean height is correct?
[A]. It lies between 150 cm and 165 cm and is closer to 150 cm.
[B]. It is greater than 165 cm.
[C]. It is exactly halfway between 150 cm and 165 cm.
[D]. It lies between 150 cm and 165 cm and is closer to 165 cm.
Q5. A bird travels an average of 44.5 km per day over 20 days. On the 21st day, it travels 55 km. What is its average daily distance over all 21 days?
[A]. 44.5 km
[B]. 45 km
[C]. 47 km
[D]. 49.75 km
Class 9 Maths Ganita Manjari Chapter 10 MCQs Set 2
Q6. The average mass of five parcels is 12 kg. A parcel weighing 16 kg is removed. What is the average mass of the remaining four parcels?
[A]. 12 kg
[B]. 11 kg
[C]. 8.8 kg
[D]. 15 kg
Q7. A group contains 30 students whose mean score is 60 and some other students whose mean score is 80. The combined mean score is 68. How many students are in the second group?
[A]. 20
[B]. 10
[C]. 40
[D]. 30
Q8. Equal masses of two sugar solutions are mixed. One contains 10% sugar by mass and the other contains 20% sugar by mass. What percentage of the mixture is sugar?
[A]. 20%
[B]. 15%
[C]. 30%
[D]. 10%
Q9. A 300 g solution containing 10% sugar by mass is mixed with a 100 g solution containing 30% sugar by mass. What percentage of the final mixture is sugar?
[A]. 20%
[B]. 12.5%
[C]. 15%
[D]. 40%
Q10. A 200 g salt solution contains 10% salt by mass. How much pure water must be added to reduce the salt concentration to 5% by mass?
[A]. 100 g
[B]. 400 g
[C]. 200 g
[D]. 20 g
Class 9 Maths Ganita Manjari Chapter 10 MCQs Set 3
Q11. Positive quantities of two salt solutions containing 4% and 10% salt by mass are mixed without any other change. Which concentration is possible for the mixture?
[A]. 14%
[B]. 12%
[C]. 7%
[D]. 2%
Q12. An alloy batch of 200 kg contains 70% copper, and another batch of 120 kg contains 50% copper. How much of a third alloy containing 45% copper must be added to obtain an alloy containing 55% copper?
[A]. 120 kg
[B]. 240 kg
[C]. 320 kg
[D]. 200 kg
Q13. A student scores 60% in internal tests, 64% in a project and 73% in the final exam. These components have weights 3 : 2 : 5, respectively. What is the final percentage score?
[A]. 73%
[B]. 65.67%
[C]. 67.3%
[D]. 66.5%
Q14. A student earns 30 out of 50 in a test and 72 out of 100 in an exam. The test and exam have equal weight in the final percentage. What is the final percentage?
[A]. 51%
[B]. 66%
[C]. 68%
[D]. 72%
Q15. A customer rates a restaurant’s food, service and ambience as 5, 3 and 4 out of 5. Their respective weights are 4 : 3 : 2. What is the overall rating, rounded to two decimal places?
[A]. 4.11
[B]. 4.33
[C]. 3.67
[D]. 4.00
Class 9 Maths Ganita Manjari Chapter 10 MCQs Set 4
Q16. What happens to a weighted mean if every weight is multiplied by 2 while all data values stay unchanged?
[A]. It doubles.
[B]. It becomes half its original value.
[C]. It remains unchanged.
[D]. It increases by 2.
Q17. The values 10 and 20 have weights 1 and 3, respectively. Each weight is increased by 1. What is the new weighted mean?
[A]. 50/3
[B]. 20
[C]. 35/2
[D]. 15
Q18. The average daily rainfall in May, June and July is 3.5 mm, 10 mm and 8.7 mm, respectively. Which expression gives the average daily rainfall over these three complete months?
[A]. (31 × 3.5 + 30 × 10 + 31 × 8.7)/3
[B]. (3.5 + 10 + 8.7)/92
[C]. (3.5 + 10 + 8.7)/3
[D]. (31 × 3.5 + 30 × 10 + 31 × 8.7)/92
Q19. After 19 complete overs, a cricket team has a run rate of 6 runs per over. It scores 12 runs in the 20th over. What is its run rate after 20 overs?
[A]. 9 runs per over
[B]. 6.3 runs per over
[C]. 12 runs per over
[D]. 6.6 runs per over
Q20. Ten customers rate a product: five give 5 stars, three give 4 stars and two give 3 stars. What is the average rating?
[A]. 4.3 stars
[B]. 3.3 stars
[C]. 4 stars
[D]. 4.5 stars
Class 9 Maths Ganita Manjari Chapter 10 MCQs Set 5
Q21. A family’s complete monthly expenditure is ₹4000 on housing, ₹3000 on food and ₹1000 on transport. In an ordinary stacked bar chart, what does the total length of its bar represent? A. ₹80
[A]. ₹8000 of total expenditure
[B]. ₹1000, the smallest expense
[C]. ₹3000, the middle expense
[D]. ₹4000, the largest expense
Q22. On an ordinary stacked expenditure bar, a food segment starts at ₹2000 and ends at ₹3500 on the scale. What is the food expenditure?
[A]. ₹5500
[B]. ₹2000
[C]. ₹3500
[D]. ₹1500
Q23. Which feature of a cluster-column chart makes comparing individual categories across groups easier than in an ordinary stacked chart?
[A]. It automatically makes all group totals equal.
[B]. Every column must represent 100%.
[C]. It removes the individual category values.
[D]. The individual columns usually begin at the same zero baseline.
Q24. Two families’ bars have equal total lengths in a 100% stacked bar chart. What can be concluded from these equal lengths alone?
[A]. Both families spent more on food than on housing.
[B]. The two families spent exactly the same amount.
[C]. Each expense category has the same percentage for both families.
[D]. Each complete bar represents 100% of its own family’s expenditure.
Q25. An electricity-use record shows 220 units for lighting, 800 for cooling, 460 for kitchen appliances and 520 for other appliances. What percentage of a 100% stacked bar should represent cooling?
[A]. 30%
[B]. 25%
[C]. 40%
[D]. 80%
Class 9 Maths Ganita Manjari Chapter 10 MCQs Set 6
Q26. A 100% stacked chart shows that 50% of Garden A’s annual flowers and 40% of Garden B’s annual flowers bloom in summer. The annual totals are unknown. Which conclusion is justified?
[A]. Garden A must have more summer flowers.
[B]. Both gardens must have the same number of summer flowers.
[C]. Garden B must have more summer flowers.
[D]. We cannot determine which garden has more summer flowers.
Q27. One garden’s annual flower total is divided into 50% summer blooms, 30% monsoon blooms and 20% winter blooms. Which statement must be true?
[A]. The garden has more summer blooms than monsoon blooms.
[B]. The garden has exactly 50 summer flowers.
[C]. The number of winter blooms equals the number of monsoon blooms.
[D]. The garden has exactly 100 flowers during the year.
Q28. A 100% stacked chart shows only category percentages for several groups. What additional information is needed to reconstruct an ordinary stacked chart showing the actual quantities?
[A]. Only the colours used in the chart
[B]. Only the number of categories
[C]. The total quantity for each group
[D]. Only the order in which categories are stacked
Q29. A 100% stacked bar represents a student’s entire 24-hour day. The learning segment occupies 25% of the bar. How many hours does it represent?
[A]. 6 hours
[B]. 4 hours
[C]. 12 hours
[D]. 8 hours
Q30. A farm initially has 60 cows, 25 sheep and 15 chickens. Later, it has 30 cows, 10 sheep and 10 chickens. Which statement correctly describes the change in the chickens’ share of all animals?
[A]. It rises from 15% to 20%, although the number of chickens falls.
[B]. It falls from 15% to 10% because 10 chickens remain.
[C]. It stays at 15% because all three animal counts fall.
[D]. It rises from 15% to 30%.
What Does Class 9 Ganita Manjari Chapter 10 Teach About Weighted Mean and Stacked Bar Charts?
Here are the 10 core facts from Class 9 Maths Ganita Manjari Part 2 Chapter 10 that every student should know:
- Weighted mean: x̄ = (w₁x₁ + w₂x₂ + … + wₙxₙ) ÷ (w₁ + w₂ + … + wₙ), where w₁, w₂, … are the weights.
- Combining two groups: If n values have average a and m values have average b, the combined average is (an + bm) ÷ (n + m).
- Average of averages: Adding group averages and dividing by the number of groups works only when all groups have the same size.
- Mixture concentration: Total quantity of the ingredient ÷ Total quantity of the mixture.
- Where the result lies: A weighted mean always lies between the smallest and largest values, closer to the one with the bigger weight.
- Custom weights: Ratios like 3:2:5 show how much each part of the data counts, for example, tests, project and final exam.
- Indian roots: Brahmagupta wrote the weighted mean formula in the Brāhmasphuṭasiddhānta (c. 628 CE) to find the mean depth of a pit, and Śrīdharācārya used it for gold purity.
- Stacked bar chart: Shows the total of each group along with the parts that make it up.
- 100% stacked bar chart: Like a pie chart, it compares proportions, not actual amounts.
- One-way conversion: A 100% stacked bar chart can be made from a stacked bar chart, but not the other way round.
Stacked Bar or 100% Stacked Bar: Which Chart Answers Which Question?
Many MCQs in this chapter ask what can be read or inferred from a chart. Use this guide:
- “Which group has the highest total?” Use a stacked bar chart. The full bar length shows the total.
- “What share of the total is this part?” Use a 100% stacked bar chart. Every bar is scaled to 100%.
- “Who spent more on one category?” A cluster-column chart is easiest, because every bar starts from zero.
- Reading middle segments: In a stacked bar, only the first segment starts at 0, so find a segment’s value by subtracting its start from its end.
- The 50% vs 40% trap: A bigger percentage does not mean a bigger number. 40% of a large total can be more than 50% of a small one.
- Totals are hidden: A 100% stacked bar chart never tells you whether two groups have the same total.
- One bar, two readings: When every bar has the same total, such as 24 hours in a day, the chart is both a stacked bar and a 100% stacked bar.
- Pie chart vs 100% stacked bar: Comparing lengths across bars is usually easier than comparing angles in separate pie charts.
The Everyday Maths Hidden Inside Chapter 10
Weighted averages are working in the background of things you use almost every day. Your annual marks, a restaurant’s star rating, a cricket team’s run rate, the average price of shares someone owns and the purity of gold in karats are all weighted means. This is not a modern idea either. Brahmagupta used it in the 7th century to find the average depth of an uneven pit, and Pṛthūdakasvāmī’s later commentary applied it to a pool dug to different depths. The second half of the chapter gives you an equally practical skill: looking at a chart and asking what it really shows and what it leaves out. These MCQs help you make both habits automatic, so you stop averaging blindly and stop trusting percentages without checking the totals behind them.
Pairing These MCQs with Your Textbook
Use this page alongside the chapter, not in place of it. After you finish the weighted mean questions, go back to Exercise Sets 10.1 to 10.3 and try the mixture problems, such as the Dead Sea salinity question or diluting the panipuri water. They use the same idea in a longer form. After the chart-based MCQs, take any stacked bar chart from the chapter and turn it into a 100% version yourself. It’s the quickest way to understand what each type shows and what it hides. Before an exam, spend five minutes estimating an answer before calculating it. If your weighted mean does not lie between the smallest and largest values, you know something has gone wrong. For worked answers to Exercise Sets 10.1 to 10.5 and the End-of-Chapter Exercises, see our NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 10 of part 2, where each problem is solved and explained.
