USP IX How Quantities Combine Test Paper with Solutions
Class IXMaths📋 Sample PaperCh 10: How Quantities Combine: Understanding DataNCERT book: Ganita Manjari
Updated 22 Oct 2026
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Class 9 Maths Ganita Manjari Chapter 10: How Quantities Combine – Test Paper with Solutions
Part II • CBSE 2026-27 • 40 Marks • 60 Minutes
18 QuestionsStep-by-step solutionsFree
This free practice test paper with solutions for Class 9 Maths Chapter 10, How Quantities Combine: Understanding Data (NCERT Ganita Manjari, Part II, session 2026-27) has 18 questions for 40 marks and is made to be finished in about 60 minutes. The paper has MCQs, short answer questions, a case study and long answer questions. Try every question on your own first. Then tap Show Answer to see the full working, with the marks for each step, and compare it with your own solution.
What this test paper covers
Average of averages: combining groups of different sizes
Weighted mean: values that carry different weights
Mixtures and concentration: finding the percentage of a substance in a mixture
Stacked and 100% stacked bar charts: reading totals and shares correctly
How the paper is arranged
Section
Type of questions
Questions
Marks each
Total
A
Multiple choice questions
8
1
8
B
Short answer questions
3
2
6
C
Short answer questions
4
3
12
D
Case study with a chart
1
4
4
E
Long answer questions
2
5
10
Total
18
40
Try each question first, then tap Show Answer to check your working.
SECTION AMultiple Choice Questions (1 mark each)8 marks
1
The average of 4 numbers is 10 and the average of 6 other numbers is 15. The average of all 10 numbers is:
1 mark
A12.5
B13
C12
D14
Answer and working
Total of the first 4 numbers = 4 × 10 = 40; total of the other 6 numbers = 6 × 15 = 90.
Average of all 10 numbers = 40 + 9010 = 13010 = 13.
Answer: (B) 13
2
200 mL of juice with 10% sugar is mixed with 300 mL of juice with 20% sugar. The concentration (percentage) of sugar in the mixture is:
1 mark
A14%
B15%
C17%
D16%
Answer and working
Sugar in the first juice = 10% of 200 = 20 mL; in the second juice = 20% of 300 = 60 mL.
Total sugar = 80 mL in 500 mL of mixture, so concentration = 80500 × 100 = 16%.
Answer: (D) 16%
3
The weighted mean of 20 and 30 with weights 1 and 3 respectively is:
Equal quantities of a 12% solution and a 20% solution are mixed. The concentration of the mixture is:
1 mark
A15%
B17%
C32%
D16%
Answer and working
For equal quantities the mixture lies exactly midway: 12 + 202 = 16%.
Answer: (D) 16%
SECTION BShort Answer Questions (2 marks each)6 marks
9
Sana scored 60 in class tests, 80 in the project and 90 in the final exam. The three parts carry weights in the ratio 1 : 2 : 2. Find her final score.
2 marks
Answer and working
Final score = 60 × 1 + 80 × 2 + 90 × 21 + 2 + 2
1 mark
= 60 + 160 + 1805 = 4005 = 80
1 mark
Answer: 80
10
The average marks of 10 students is 50 and the average marks of 20 other students is 65. Find the average marks of all 30 students.
2 marks
Answer and working
Total marks of the 10 students = 10 × 50 = 500; of the 20 students = 20 × 65 = 1300.
1 mark
Average of all 30 students = 500 + 130010 + 20 = 180030 = 60.
1 mark
Answer: 60 marks
11
A shopkeeper mixes 2 kg of rice costing ₹30 per kg with 3 kg of rice costing ₹40 per kg. Find the cost of 1 kg of the mixture.
2 marks
Answer and working
Total cost = 2 × 30 + 3 × 40 = 60 + 120 = ₹180 for 2 + 3 = 5 kg.
1 mark
Cost of 1 kg = 1805 = ₹36.
1 mark
Answer: ₹36 per kg
SECTION CShort Answer Questions (3 marks each)12 marks
12
A jeweller melts 40 g of a gold alloy that is 75% pure with 60 g of a gold alloy that is 50% pure. Find the purity (percentage of pure gold) of the new alloy.
3 marks
Answer and working
Pure gold in the first alloy = 75% of 40 g = 30 g; in the second alloy = 50% of 60 g = 30 g.
1 mark
Total pure gold = 30 + 30 = 60 g, and total alloy = 40 + 60 = 100 g.
1 mark
Purity = 60100 × 100 = 60%.
1 mark
Answer: 60%
13
A restaurant gives weights 5, 3 and 2 to food, service and ambience. A customer gives food 4 stars, service 5 stars and ambience 3 stars.
3 marks
(a)Find the weighted rating.[2]
(b)Find the simple average of the three ratings.[1]
How much pure water must be added to 100 mL of a 20% sugar solution to make it a 10% sugar solution? (Pure water has 0% sugar.)
3 marks
Answer and working
Sugar in the solution = 20% of 100 = 20 mL. Adding water does not change the amount of sugar.
1 mark
Let w mL of water be added. Then 20100 + w = 10100
1 mark
100 + w = 200, so w = 100. Check: 20 mL of sugar in 200 mL is 10%.
1 mark
Answer: 100 mL of water
15
Group P has 8 students with average marks 52 and Group Q has 2 students with average marks 82. Rani says, “The average of all 10 students is 52 + 822 = 67.” Is Rani correct? Find the correct average and give the reason.
3 marks
Answer and working
Rani is not correct.
1 mark
Marks of P = 8 × 52 = 416; marks of Q = 2 × 82 = 164; total = 580 for 10 students.
1 mark
Correct average = 58010 = 58. Rani treated both groups as equally important, but Group P has four times as many students, so it must count more. A simple average of two averages is correct only when the groups are of the same size.
1 mark
Answer: No; the correct average is 58 marks
SECTION DCase Study (4 marks)4 marks
16
Family A and Family B noted their monthly spending in four groups: Food, Rent, Education and Others. The 100% stacked bar chart shows the share of each group. The total monthly spending of Family A is ₹20,000 and of Family B is ₹30,000.
4 marks
(i)Which family spends a larger share of its spending on food?[1]
(ii)Find the amount (in ₹) that each family spends on food.[1]
(iii)Family A says, “We spend more money on food than Family B, because the food part of our bar is longer.” Is this correct? Explain using your answer to (ii).[2]
Answer and working
(i) Family A. Its food share is 40%, which is more than 30% for Family B.
1 mark
(ii) Family A: 40% of ₹20,000 = ₹8,000. Family B: 30% of ₹30,000 = ₹9,000.
1 mark
(iii) No, the statement is not correct. A 100% stacked bar chart shows only shares (percentages), not rupee amounts. Family B spends ₹9,000 on food, which is more than the ₹8,000 of Family A, although B’s food part is shorter, because B’s total spending is bigger.
2 marks
Answer: (i) Family A (ii) ₹8,000 and ₹9,000 (iii) not correct
SECTION ELong Answer Questions (5 marks each)10 marks
17
Bottle X holds 600 mL of lemonade with 15% jaggery. Bottle Y holds 400 mL of lemonade with 20% jaggery. Both are poured into one big jug.
5 marks
(a)Find how many mL of jaggery are in Bottle X and in Bottle Y.[2]
(b)Find the concentration (percentage) of jaggery in the jug.[2]
(c)Is the mixture closer to 15% or to 20%? Give a reason.[1]
Answer and working
(a) Jaggery in X = 15% of 600 = 90 mL.
1 mark
Jaggery in Y = 20% of 400 = 80 mL.
1 mark
(b) Total jaggery = 90 + 80 = 170 mL in 600 + 400 = 1000 mL.
1 mark
Concentration = 1701000 × 100 = 17%.
1 mark
(c) Closer to 15%, because Bottle X has the larger quantity (600 mL against 400 mL), and the larger quantity pulls the concentration towards its own value.
1 mark
Answer: (a) 90 mL and 80 mL (b) 17% (c) closer to 15%
18
The stacked bar chart shows the number of books read by Class IX-A and Class IX-B in a month.
5 marks
(a)How many Science books did Class IX-B read?[1]
(b)Find the total number of books read by each class, and say how many more books IX-B read than IX-A.[2]
(c)Priya says, “IX-A read fewer Story books than IX-B, so IX-A likes Story books less.” Find the share (percentage) of Story books in each class and say whether Priya is correct.[2]
Answer and working
(a) The Science part of the IX-B bar is 30 books long.
1 mark
(b) Total for IX-A = 25 + 15 + 10 = 50 books. Total for IX-B = 40 + 30 + 30 = 100 books.
1 mark
IX-B read 100 − 50 = 50 more books than IX-A.
1 mark
(c) Share of Story books in IX-A = 2550 × 100 = 50%; in IX-B = 40100 × 100 = 40%.
1 mark
Priya is not correct. IX-A read fewer Story books (25 against 40), but IX-A read only 50 books in all, so Story books are a larger share (50%) of its reading than of IX-B’s (40%).
1 mark
Answer: (a) 30 (b) 50 and 100 books; 50 more (c) 50% and 40%; Priya is not correct
Key ideas and formulas from Chapter 10
Average of groups. Never add two averages and divide by 2 unless the groups are the same size. Use the totals: combined average = n1 × a1 + n2 × a2n1 + n2, where n is the number of members and a is the average of each group.
Weighted mean. Weighted mean = w1x1 + w2x2 + …w1 + w2 + …. If every weight is multiplied (or divided) by the same number, the weighted mean does not change.
Concentration of a mixture. Concentration = amount of the substancetotal quantity of the mixture × 100. Equal quantities give the midpoint of the two concentrations. The larger quantity pulls the answer towards its own concentration. Pure water has 0% of any substance.
Stacked and 100% stacked bar charts. In a stacked bar the whole length is the total of its parts. In a 100% stacked bar every bar has the same length, so it shows only the shares. To compare amounts, you also need the totals.
Common mistakes to avoid
Taking the simple average of two group averages when the groups have different sizes.
Forgetting to multiply each value by its weight before adding.
Reading a longer part in a 100% stacked bar as a bigger amount.
Frequently asked questions
What is a weighted mean?
A weighted mean is an average in which some values count more than others. Each value is multiplied by its weight, the results are added, and the total is divided by the sum of the weights.
Why can we not simply average two averages?
Because the two groups may have different numbers of members. A group with more members should count more, so we add the total marks (or total values) of both groups and divide by the total number of members.
How do I find the concentration of a mixture?
Find the amount of the substance in each part, add these amounts, divide by the total quantity of the mixture and multiply by 100 to get a percentage.
What is the difference between a stacked bar chart and a 100% stacked bar chart?
A stacked bar chart shows the actual amounts, so the full bar length is the total. A 100% stacked bar chart scales every bar to 100%, so it shows only the share of each part and hides the actual totals.
How much time should students take for this paper?
The paper is designed for about 60 minutes for 40 marks. Students can attempt the questions in order and use Show Answer only after finishing each question.
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