Important Questions for Class 9 Maths (Ganita Manjari II) Chapter 10 How Quantities Combine: Understanding Data 2026-27

Understanding data becomes easier with regular practice. The important questions for Class 9 Maths Chapter 10 help students compare quantities, interpret information and apply mathematical concepts to solve problems accurately.

Class 9 Maths Chapter 10 Important Questions – MCQs

Q1. Two groups have average marks of 40 and 60. If the first group has 10 students and the second group has 20 students, what is the combined average?

A) 50

B) 53.33

C) 55

D) 60

Answer: B) 53.33

Solution:

Combined average = $$\frac{40\times10+60\times20}{10+20}$$

= $$\frac{400+1200}{30}$$

= $$\frac{1600}{30}$$

= 53.33

The combined average is 53.33 marks.

Q2. Two solutions containing 12% and 28% salt are mixed in equal quantities. What will be the salt concentration of the new solution?

A) 16%

B) 18%

C) 20%

D) 24%

Answer: C) 20%

Solution:

Since equal quantities are mixed, the final concentration is the arithmetic mean of the two concentrations.

Concentration = $$\frac{12+28}{2}$$

= 20%

The new solution contains 20% salt.

Q3. Which type of chart is most suitable for comparing both the total sales and the contribution of different products to those sales?

A) Pie chart

B) Stacked bar chart

C) Line graph

D) Pictograph

Answer: B) Stacked bar chart

Explanation: A stacked bar chart shows the total value through the full length of a bar. Its smaller sections show how much each product contributes to that total.

Q4. Two schools have different numbers of students. A 100% stacked bar chart shows that 40% of students in School A and 30% in School B travel by bus. Which conclusion is correct?

A) More students travel by bus in School A.

B) More students travel by bus in School B.

C) Both schools have the same number of bus users.

D) The actual number of bus users cannot be determined without knowing the total students.

Answer: D) The actual number of bus users cannot be determined without knowing the total students.

Explanation: A 100% stacked bar chart shows proportions, not actual totals. School B may have more bus users if it has a much larger number of students.

Class 9 Maths Chapter 10 Very Short Answer Questions

Q5. What is a weighted average? Write its formula.

Answer:

A weighted average is an average in which different values are given different levels of importance or weights.

The formula is:

$$\bar{x}=\frac{w_1x_1+w_2x_2+\cdots+w_nx_n}{w_1+w_2+\cdots+w_n}$$

Here, $$x_1,x_2,\ldots,x_n$$ are the values and $$w_1,w_2,\ldots,w_n$$ are their respective weights.

Q6. Three groups have the same number of students. Their average scores are 45, 55 and 65. Find the combined average score.

Answer:

Since all three groups have equal numbers of students, we can take the simple average of their averages.

Combined average = $$\frac{45+55+65}{3}$$

= $$\frac{165}{3}$$

= 55

The combined average score is 55.

Q7. What is the main difference between a stacked bar chart and a 100% stacked bar chart?

Answer:

A stacked bar chart shows actual values and their totals. A 100% stacked bar chart shows the percentage contribution of each part, with every complete bar representing 100%.

Q8. A student's scores are 70 and 90, with weights 2 and 3 respectively. Find the weighted average.

Answer:

Weighted average = $$\frac{70\times2+90\times3}{2+3}$$

= $$\frac{140+270}{5}$$

= 82

The weighted average is 82.

Class 9 Maths Chapter 10 Short Answer Questions

Q9. The average age of 12 members of a club is 16 years. Four new members with an average age of 21 years join the club. Find the new average age.

Solution:

Step 1: Find the total age of the original members.

Total age = 12 × 16 = 192 years

Step 2: Find the total age of the new members.

Total age = 4 × 21 = 84 years

Step 3: Find the combined average.

New average = $$\frac{192+84}{12+4}$$

= $$\frac{276}{16}$$

= 17.25 years

Answer: The new average age is 17.25 years.

Q10. A fruit juice mixture contains 300 mL of juice with 20% fruit concentrate and 200 mL of juice with 35% fruit concentrate. Find the concentration of fruit in the final mixture.

Solution:

Step 1: Find the fruit concentrate in the first quantity.

300 × 20% = 60 mL

Step 2: Find the fruit concentrate in the second quantity.

200 × 35% = 70 mL

Step 3: Find the total concentrate and total mixture.

Total concentrate = 60 + 70 = 130 mL

Total mixture = 300 + 200 = 500 mL

Step 4: Calculate the percentage.

Concentration = $$\frac{130}{500}\times100$$

= 26%

Answer: The final mixture contains 26% fruit concentrate.

Q11. A school calculates the final score using assignments, projects and examinations in the ratio 2 : 3 : 5. A student scores 80%, 70% and 90% respectively. Find the final percentage.

Solution:

The given weights are 2, 3 and 5.

Weighted score = $$\frac{80\times2+70\times3+90\times5}{2+3+5}$$

= $$\frac{160+210+450}{10}$$

= $$\frac{820}{10}$$

= 82%

Answer: The student's final percentage is 82%.

Q12. A library records the number of books issued in three categories during two weeks.

(a) Find the total books issued in each week.

(b) Which week had more books issued?

(c) Explain why a stacked bar chart would be suitable for this data.

Solution:

(a)

Week 1 total = 30 + 20 + 10 = 60 books

Week 2 total = 45 + 25 + 20 = 90 books

(b)

Difference = 90 − 60 = 30 books

Week 2 had 30 more books issued.

(c)

A stacked bar chart would show the total books issued each week while also showing the contribution of Fiction, Science and History books.

Answer: Week 1: 60 books; Week 2: 90 books. A stacked bar chart helps compare both weekly totals and categories.

Q13. A school has 400 students, of whom 160 participate in sports, 120 in music, 80 in art and 40 in dance. Calculate the percentage share of each activity for a 100% stacked bar chart.

Solution:

Total students = 400

Sports = $$\frac{160}{400}\times100=40%$$

Music = $$\frac{120}{400}\times100=30%$$

Art = $$\frac{80}{400}\times100=20%$$

Dance = $$\frac{40}{400}\times100=10%$$

Check: 40% + 30% + 20% + 10% = 100%

Answer:

These percentages can be used to divide one complete bar into four sections.

Class 9 Maths Chapter 10 Long Answer Questions

Q14. A company has three departments with the following numbers of employees and average monthly salaries.

(a) Find the average monthly salary of all employees.

(b) Explain why taking the simple average of the three departmental averages would be incorrect.

Solution:

(a) Find the combined average salary.

Step 1: Calculate the total salary of each department.

Department A = 20 × 25,000 = ₹5,00,000

Department B = 30 × 30,000 = ₹9,00,000

Department C = 50 × 40,000 = ₹20,00,000

Step 2: Calculate the total salary.

Total salary = ₹5,00,000 + ₹9,00,000 + ₹20,00,000

= ₹34,00,000

Step 3: Calculate the total number of employees.

20 + 30 + 50 = 100

Step 4: Find the combined average.

Average salary = $$\frac{3400000}{100}$$

= ₹34,000

(b) Why is the simple average incorrect?

The simple average of the three departmental averages is:

$$\frac{25000+30000+40000}{3}$$

= ₹31,666.67

This is incorrect because the departments have different numbers of employees. Department C has the largest number of employees, so its average salary must have a greater influence on the combined average.

Answer: The correct average monthly salary is ₹34,000

Q15. A container has 8 litres of a solution containing 25% salt. How much pure water must be added to reduce the salt concentration to 10%?

Solution:

Step 1: Find the amount of salt in the original solution.

Salt = 25% of 8 litres

= $$\frac{25}{100}\times8$$

= 2 litres

Step 2: Let the quantity of water added be $$x$$ litres.

After adding water:

Total mixture = $$(8+x)$$ litres

The quantity of salt remains 2 litres because pure water contains no salt.

Step 3: Form the equation.

$$\frac{2}{8+x}=\frac{10}{100}$$

$$\frac{2}{8+x}=0.1$$

Step 4: Solve.

2 = 0.1(8 + x)

2 = 0.8 + 0.1x

1.2 = 0.1x

$$x=12$$

Step 5: Verify.

Final mixture = 8 + 12 = 20 litres

Salt concentration = $$\frac{2}{20}\times100=10%$$

Answer: 12 litres of pure water must be added.

Q16. Two schools record how their students travel to school. The data is given below.

(a) Find the percentage of students using each mode of transport in both schools.

(b) Prepare the data required for a 100% stacked bar chart.

(c) Which school has a greater percentage of students travelling by bus?

(d) Which school has more students walking to school?

Solution:

(a) Calculate the percentages.

For School A:

Bus = $$\frac{120}{200}\times100=60%$$

Bicycle = $$\frac{60}{200}\times100=30%$$

Walking = $$\frac{20}{200}\times100=10%$$

For School B:

Bus = $$\frac{90}{300}\times100=30%$$

Bicycle = $$\frac{90}{300}\times100=30%$$

Walking = $$\frac{120}{300}\times100=40%$$

(b) Data for the 100% stacked bar chart:

Draw two equal-length bars representing 100% each. Divide the bars into sections using the percentages in the table.

(c) School A has a greater percentage of students travelling by bus (60% compared with 30%).

(d) School B has more students walking to school (120 compared with 20).

Answer: School A has the higher proportion of bus users, while School B has more students walking to school, both in number and percentage.

How to Solve Class 9 Maths Chapter 10 Data-Based Questions Easily?

Students learn to organise numerical information, compare values and draw meaningful conclusions from How Quantities Combine: Understanding Data. Practising these skills helps students solve data-related problems more accurately.

Follow these tips while solving questions:

• Read the Data Carefully: Identify the given values and what the question asks.

• Compare Quantities: Look for differences, totals and relationships between values.

• Identify Patterns: Observe how the numbers change and what they indicate.

• Show Your Calculations: Write each step clearly to avoid mistakes.

• Check Your Answers: Make sure the result matches the given information.

Why Choose Vedantu's Class 9 Maths Chapter 10 Important Questions PDF?

Vedantu's Class 9 Maths Chapter 10 Important Questions with Solutions helps students practise How Quantities Combine: Understanding Data through focused questions and clear explanations.

Here's how the PDF helps students:

• Chapter-Focused Practice: Work on important data-based problems in one place.

• Solved Answers: Understand the steps involved in solving each question.

• Exam Preparation: Practise MCQs, short-answer and long-answer questions.

• Self-Assessment: Check solutions and identify mistakes independently.

• Easy PDF Access: Download the questions and practise at your own pace.

The Class 9 Maths Chapter 10 Important Questions PDF helps students prepare for the 2026-27 school exams with organised practice and solutions.

Important Study Materials for Class 9 Maths (Ganita Manjari II) Chapter 10 How Quantities Combine: Understanding Data

CBSE Class 9 Maths Chapter-wise Important Questions

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