CBSE Class 8 Mathematics Data Handling Practice Paper Assignment Set 12 with Answers (Old NCERT Syllabus)

This Class 8 Maths Data Handling practice paper is a 40-mark test of 17 questions arranged in Sections A to E, and every question comes with a step-by-step answer. It follows the earlier (old) NCERT Class 8 Maths syllabus, so it is useful for state-board students and for revision of this chapter. It focuses on reading and drawing pie charts (central angles, amounts from angles and percentages) and on simple probability with buttons, balls, slips, dice and letters.

Section A: Multiple Choice Questions (1 Mark Each)

Section B: Short Answer Questions (2 Marks Each)

Question 7. A bag contains 7 white, 4 red, and 3 green balls. A ball is randomly drawn from the bag. Find the probability that it is a white ball.
Answer:
Total number of balls = 7 + 4 + 3 = 14.
Number of white balls = 7.
P(white ball) = \( \frac{7}{14} = \frac{1}{2} \).
So the probability is \( \frac{1}{2} \).
In simple words: Half of the 14 balls are white, so the chance is 1/2.

Teacher's Note:
1. Count all the balls for the total number of outcomes.
2. Write the probability in lowest terms.

Question 8. Numbers 1 to 10 are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. Find the probability of getting a factor of number 6.
Answer:
Total number of outcomes = 10.
Factors of 6 among 1 to 10 are 1, 2, 3 and 6, so there are 4 favourable outcomes.
P(factor of 6) = \( \frac{4}{10} = \frac{2}{5} \).
So the probability is \( \frac{2}{5} \).
In simple words: 4 of the 10 slips (1, 2, 3, 6) are factors of 6, so the chance is 4/10 = 2/5.

Teacher's Note:
1. 1 and 6 itself are both factors of 6; do not miss them.
2. List the favourable outcomes before counting them.

Question 9. Out of 500 lottery tickets, 10 are prize winning tickets. A person buys a ticket. Find the probability of getting a prize winning ticket.
Answer:
Total number of outcomes = 500.
Number of prize winning tickets = 10.
P(prize) = \( \frac{10}{500} = \frac{1}{50} \).
So the probability is \( \frac{1}{50} \).
In simple words: 10 tickets out of 500 win, which is 1 chance in 50.

Teacher's Note:
1. Probability is always between 0 and 1.
2. The probability of not winning is 1 − 1/50 = 49/50.

Section C: Short Answer Questions (3 Marks Each)

Question 10. The following pie chart depicts the expenditure of a state government under different heads.
(a) If the total spending is 10 crores, how much money was spent on roads?
(b) How many times is the amount of money spent on education compared to the amount spent on roads?
(c) What fraction of the total expenditure is spent on both roads and public welfare together?

Answer:
(a) Money spent on roads = 10% of ₹ 10 crore = \( \frac{10}{100} \times 10 \) crore = ₹ 1 crore.
(b) Education = 25% and roads = 10%, so \( \frac{25}{10} = 2.5 \).
Money spent on education is 2.5 times the money spent on roads (₹ 2.5 crore compared with ₹ 1 crore).
(c) Roads + public welfare = 10% + 20% = 30% = \( \frac{30}{100} = \frac{3}{10} \).
So \( \frac{3}{10} \) of the total expenditure is spent on roads and public welfare together.
In simple words: Work with the percentages: roads are 10% of 10 crore = 1 crore, education is 25 ÷ 10 = 2.5 times roads, and roads + welfare = 30% = 3/10.

Teacher's Note:
1. Percentages in a pie chart are parts of 100, so compare them directly.
2. 10 crore = 10,00,00,000, so 1 crore = 1,00,00,000.

Question 11. A pie diagram of the marks secured by a student in Maths, English, Physics and Chemistry is shown here. Read the graph and find the marks in Chemistry secured by the student.

Answer:
Let the central angle for Chemistry be x°.
The angles add up to 360°: 100° + 75° + 100° + x° = 360°.
275° + x° = 360°, so x = 85°.
A sector of 100° (Maths) stands for 80 marks, so 1° stands for \( \frac{80}{100} = 0.8 \) marks.
Chemistry marks = 85 × 0.8 = 68.
So the student scored 68 marks in Chemistry.
In simple words: Chemistry's angle is 360° − 275° = 85°, and since 100° means 80 marks, 85° means 68 marks.

Teacher's Note:
1. Find the missing angle from the total of 360° first.
2. Use the known sector (Maths) to find the marks for 1°.
3. Total marks = 360 × 0.8 = 288, and 85/360 × 288 = 68 as a check.

Question 12. Instead of numbers, the letters in the word CHANCE were stuck on a die. Find the probability of rolling: (i) letter H (ii) a vowel (iii) a consonant
Answer:
The six faces show C, H, A, N, C, E, so there are 6 equally likely outcomes.
(i) H appears on 1 face: P(H) = \( \frac{1}{6} \).
(ii) Vowels are A and E (2 faces): P(vowel) = \( \frac{2}{6} = \frac{1}{3} \), so \( \frac{1}{3} \).
(iii) Consonants are C, H, N, C (4 faces): P(consonant) = \( \frac{4}{6} = \frac{2}{3} \), so \( \frac{2}{3} \).
In simple words: Count the faces: H on 1, vowels on 2 and consonants on 4 of the 6 faces.

Teacher's Note:
1. C appears twice, so it counts as two faces.
2. P(vowel) + P(consonant) = 1/3 + 2/3 = 1, a quick check.

Question 13. A die is rolled once. What is the probability that the number on top will be (a) odd (b) greater than 5 (c) a multiple of 3
Answer:
Possible outcomes: 1, 2, 3, 4, 5, 6, so there are 6 outcomes.
(a) Odd numbers: 1, 3, 5. P(odd) = \( \frac{3}{6} = \frac{1}{2} \), so \( \frac{1}{2} \).
(b) Greater than 5: only 6. P = \( \frac{1}{6} \).
(c) Multiples of 3: 3 and 6. P = \( \frac{2}{6} = \frac{1}{3} \), so \( \frac{1}{3} \).
In simple words: List the six outcomes and count how many fit each condition.

Teacher's Note:
1. 'Greater than 5' does not include 5.
2. Always reduce the fraction to its lowest terms.

Section D: Long Answer Questions (4 Marks Each)

Teacher's Note:
1. Each 1% is 3.6°, so 25% = 90°, 30% = 108° and 15% = 54°.
2. Label every sector with its name and percentage.

Question 15. The pie chart shows the expenditure on various items of a family during a month. The total amount spent is ₹ 20,000.
(a) Find the amount spent on clothes.
(b) How much more amount is spent on food than on education?
(c) On which item was the expenditure maximum?
(d) What is the amount spent on rent?

Answer:
Amount on an item = (central angle ÷ 360°) × ₹ 20,000.
(a) Clothes = \( \frac{36}{360} \times 20000 \) = ₹ 2000.
(b) Food = \( \frac{108}{360} \times 20000 \) = ₹ 6000; Education = \( \frac{72}{360} \times 20000 \) = ₹ 4000.
Food − Education = ₹ 6000 − ₹ 4000 = ₹ 2000 more on food.
(c) Food has the largest angle (108°), so the expenditure was maximum on food.
(d) Rent = \( \frac{90}{360} \times 20000 \) = ₹ 5000.
In simple words: Each degree stands for 20000 ÷ 360 rupees; multiply by the angle of each item.

Teacher's Note:
1. The biggest sector (largest angle) always shows the biggest amount.
2. Check: 54° + 72° + 36° + 90° + 108° = 360°.

Question 16. A bag contains 10 red, 5 blue and 7 green balls. A ball is drawn at random. Find the probability of this ball being a (i) red ball (ii) green ball (iii) blue ball (iv) not a blue ball
Answer:
Total number of balls = 10 + 5 + 7 = 22.
(i) P(red) = \( \frac{10}{22} = \frac{5}{11} \), so \( \frac{5}{11} \).
(ii) P(green) = \( \frac{7}{22} \).
(iii) P(blue) = \( \frac{5}{22} \).
(iv) Balls that are not blue = 10 + 7 = 17, so P(not blue) = \( \frac{17}{22} \).
In simple words: There are 22 balls; count the balls of each kind and divide by 22.

Teacher's Note:
1. P(not blue) = 1 − P(blue) = 1 − 5/22 = 17/22.
2. The probabilities of red, green and blue add to 1.

Section E: Case Study Based Question (4 Marks)

Question 17. The following pie chart represents the distribution of proteins in parts of the human body.
(a) What is the ratio of the distribution of proteins in the muscles to that of proteins in the bones? (1)
(b) What is the central angle of the sector (in the above pie chart) representing skin and bones together? (1)
(c) What is the central angle of the sector (in the above pie chart) representing hormones, enzymes and other proteins? (2)
Answer:
(a) Muscles : Bones = \( \frac{1}{3} : \frac{1}{6} \). Multiply both by 6: 2 : 1. So the ratio is 2 : 1.
(b) Skin + bones = \( \frac{1}{10} + \frac{1}{6} = \frac{3}{30} + \frac{5}{30} = \frac{8}{30} = \frac{4}{15} \).
Central angle = \( \frac{4}{15} \times 360^\circ \) = 96°.
(c) Hormones, enzymes and other proteins = \( 1 - \left(\frac{1}{3} + \frac{1}{10} + \frac{1}{6}\right) = 1 - \frac{10 + 3 + 5}{30} = 1 - \frac{18}{30} = \frac{2}{5} \).
Central angle = \( \frac{2}{5} \times 360^\circ \) = 144°.
In simple words: Muscles are twice bones (2 : 1); skin and bones are 4/15 of the circle (96°); the rest is 2/5 of the circle (144°).

Teacher's Note:
1. Angles: muscles 120°, skin 36°, bones 60°, others 144°, which add to 360°.
2. The whole pie is 1, so the missing part is 1 minus the known parts.