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Class 9 Maths: How Quantities Combine, Understanding Data, 8 practice questions with answers

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These are 8 practice questions on Chapter 10, How Quantities Combine: Understanding Data, of the new NCERT Class 9 Maths textbook, Ganita Manjari, Part II (First Edition, August 2026). Each has a worked answer and the textbook page it comes from. They cover the average of two groups of different sizes, when averaging the averages does and does not work, the concentration of a mixture, finding how much of a mixture to add, what weights do to an average, and what a stacked bar chart and a 100% stacked bar chart can and cannot tell you. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every number was re-computed by a test script and none of the numbers is taken from the chapter, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Manjari, Grade 9, Part II, Chapter 10, printed pages 8 to 36):

Averages of groups

Question 1. Crate A holds 56 mangoes with an average mass of 245 g. Crate B holds 112 mangoes with an average mass of 302 g. What is the average mass of all the mangoes together?

Answer: 283 g. Total mass in crate A = 56 × 245 = 13720 g; in crate B = 112 × 302 = 33824 g. Combined average = (13720 + 33824) ÷ (56 + 112) = 47544 ÷ 168 = 283 g. It is closer to 302 g than to 245 g because crate B has more mangoes. (Combined average (an + bm) ÷ (n + m), pages 8 and 9.)

Question 2. In a survey, 47 children from one school read for an average of 52 minutes a day, and 94 children from another school read for an average of 91 minutes a day. A student says the average for all the children is 71.5 minutes, the value midway between 52 and 91. Is that right? Find the correct average.

Answer: no; the correct average is 78 minutes. Averaging the two averages treats both schools as equal, but the second school has twice as many children. Combined average = (47 × 52 + 94 × 91) ÷ (47 + 94) = (2444 + 8554) ÷ 141 = 10998 ÷ 141 = 78 minutes. Averaging the averages would only work if the two groups were the same size. (Average of averages, pages 9 and 10.)

Mixtures

Question 3. 450 g of a nut mix that is 56% almonds is mixed with 650 g of a nut mix that is 78% almonds. What percentage of the new mix is almonds?

Answer: 69%. Almonds in the first mix = 0.56 × 450 = 252 g; in the second = 0.78 × 650 = 507 g. Concentration = (252 + 507) ÷ (450 + 650) = 759 ÷ 1100 = 0.69, that is 69%. It is closer to 78% than to 56% because more of the 78% mix was used. (Concentration of a mixture, pages 11 and 12.)

Question 4. You have 450 g of the 56% almond mix. How much of the 78% almond mix must you add so that the new mix is 69% almonds?

Answer: 650 g. Let y grams of the 78% mix be added. Almonds: 252 + 0.78y; total mass: 450 + y. For a 69% mix, 252 + 0.78y = 0.69 × (450 + y) = 310.5 + 0.69y. So 0.78y − 0.69y = 310.5 − 252, that is 0.09y = 58.5, and y = 58.5 ÷ 0.09 = 650 g. This agrees with the mix in the question above. (Solving for an unknown quantity in a mixture, page 12.)

Weights and charts

Question 5. (a) A school's final mark combines a project, a mid-term test and a final exam using weights. A student did best in the final exam and worst in the project. If the school gives the final exam a larger weight than before, and keeps the other weights the same, will the student's final mark go up or down? Explain without calculating. (b) The student scored 66 in the project, 78 in the mid-term and 95 in the final exam. Find the final mark when the weights are 1 : 2 : 4, and again when the final exam's weight is raised to 6 (weights 1 : 2 : 6).

Answer: (a) it goes up; (b) 86 with weights 1 : 2 : 4, and 88 with weights 1 : 2 : 6. (a) The weighted mean is pulled towards the values with the larger weights. Giving more weight to the final exam, the student's best score, moves the weighted mean towards that score, so the final mark rises. (b) With weights 1 : 2 : 4: (66 × 1 + 78 × 2 + 95 × 4) ÷ (1 + 2 + 4) = (66 + 156 + 380) ÷ 7 = 602 ÷ 7 = 86. With weights 1 : 2 : 6: (66 + 156 + 95 × 6) ÷ (1 + 2 + 6) = (66 + 156 + 570) ÷ 9 = 792 ÷ 9 = 88. The mark rose from 86 to 88, as part (a) predicted. (Weights as relative importance, page 14; the weighted mean, page 12.)

Question 6. Shop P sold 143 notebooks, 86 pens and 57 erasers in a week. Shop Q sold 98 notebooks, 152 pens and 61 erasers. In a stacked bar chart with one bar per shop, which bar is longer? Does that mean Q sold more of every item?

Answer: Q's bar is longer, but Q did not sell more of every item. The full length of each stacked bar is the shop's total: P = 143 + 86 + 57 = 286 and Q = 98 + 152 + 61 = 311, so Q's bar is longer. But P sold more notebooks (143 against 98). A stacked bar chart shows the totals and keeps the parts visible, so both facts can be read from it, though comparing one item, such as notebooks, across the bars is harder than comparing totals, because only the first part of each bar starts from zero. (Stacked bar charts, page 20.)

Question 7. A 100% stacked bar chart shows that fiction was 58% of the books lent by School A's library and 46% of those lent by School B's library. School A lent 350 books in all and School B lent 650. Which school lent more fiction books, and what does this tell you about reading a 100% stacked bar chart?

Answer: School B, 299 fiction books against School A's 203. School A: 0.58 × 350 = 203 fiction books. School B: 0.46 × 650 = 299 fiction books. B lent more fiction even though its percentage is smaller, because it lent more books in all. A 100% stacked bar chart compares shares, not amounts: to compare actual numbers you also need the totals. (100% stacked bar charts, pages 23 and 25.)

Question 8. You have the number of mangoes, guavas and bananas sold by three fruit sellers in a month. Which kind of chart would you draw (a) to see which seller sold the most fruit in all, and how much of it was each fruit; (b) to see which seller's sales had the largest share of bananas? If you are given only the 100% stacked bar chart, can you work out how many guavas each seller sold?

Answer: (a) a stacked bar chart; (b) a 100% stacked bar chart; no. A stacked bar chart shows the totals and the parts that make them up. A 100% stacked bar chart gives every seller a bar of the same length, so it compares proportions, such as the share of bananas. A stacked bar chart can be turned into a 100% stacked bar chart, but not the other way round, because the 100% chart does not show the totals. (Stacked bar charts, page 20; 100% stacked bar charts, page 23; chapter summary, page 36.)

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Sources

All opened and read on 22 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 7.

The rules and the formula are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.