Class 8 SESSION ENDING EXAMINATION (2026) SAMPLE PAPER-11 WITH ANSWERS

 Class 8 SESSION ENDING EXAMINATION (2026)  SAMPLE PAPER-11 WITH ANSWERS

SAMPLE PAPER 11

SECTION A

1. What is the digital root of the number 489710?
   a) 1 b) 2 c) 9 d) 11

2. A number is divisible by 9 if and only if:
   A) Its units digit is 0 or 9 B) It is an even number C) The sum of its digits is divisible by 9 D) It is also divisible by 11

3. What is the correct expansion of the identity (a+m)(b+n)?
   a) ab + mn b) ab + mb + an + mn c) ab + an + m d) am + bn + ab

4. According to Brahmagupta, what is the term for "multiplication by parts" using the distributive property?
   a) Ista-gunana b) Khanda-gunanam c) Ganita Prakash d) Brahmashputasiddhanta

5. What is the simplest form of the ratio 60:40?
   a) 20:1 b) 3:2 c) 1.5:1 d) 6:4

6. Two ratios a:b and c:d are proportional (indicated by the '::' symbol) if and only if:
   a) a + d = b + c b) ad = bc c) a = c and b = d d) Their terms are even numbers

7. Which of the following is the decimal equivalent of 40%?
   a) 4.0 b) 0.04 c) 0.4 d) 0.44

8. The simplest form of 36/48 is:
   a) 6/8 b) ¾ c) 3.099 d) 3.909

9. Which of the following sets of numbers is a Baudhāyana-Pythagoras triple?
   a) (1, 2, 3) b) (5, 12, 13) c) (2, 3, 4) d) (7, 8, 10)

10. The number √2 has which of the following properties?
    a) It is a terminating decimal b) It can be expressed as a fraction m/n where m and n are positive integers
    c) It lies between 1.414 and 1.415 but cannot be a terminating decimal d) It is equal to 1.5

11. A parallelogram has a base of 10 cm and a corresponding height of 6 cm. What is its area?
    a) 16 cm² b) 32 cm² c) 60 cm² d) 30 cm²

12. The standard unit of area is:
    a) metre b) square metre c) centimetre d) kilogram

13. A rhombus has diagonals measuring 10 cm and 24 cm. What is the area of this rhombus?
    a) 240 cm² b) 120 cm² c) 68 cm² d) 34 cm²

Assertion-Reason:

14. Assertion: (x+3)(x+5) = x² + 8x + 15
    Reason: Each term of the first bracket is multiplied with each term of the second bracket.

15. Assertion: The fraction 15/20 is simply 3/4 in disguise.
    Reason: Equivalent fractions are formed by multiplying or dividing the numerator and the denominator of a given fraction by the same non-zero number.

SECTION B (2 marks each)

16. If a number is divisible by 12, explain why it must also be divisible by 3 and 4.

17. Calculate the digital root for the number 320185.

18. Using the distributive property, explain the step-by-step process for multiplying 94×11 in a single line.
    OR
    Show how the product ab changes when both a and b are increased by 1. Write the final expanded expression.

19. Express 50% of a quantity 8 as a multiplication of its unit fraction and simplify the result.
    OR
    In a school, 15 of the 80 students come to school by walking. What percentage of the students come by walking?

20. The length of the two equal sides of an isosceles right triangle is 3 cm. Find the length of the hypotenuse.

SECTION C (3 marks each)

21. The sum of four consecutive numbers is 34. What are these numbers?
    OR
    If 31z5 is a multiple of 9, where z is a digit, what is the value of z? Explain why there are two answers to this problem.

22. A car travels 90 km in 150 minutes. Show the conversion of 4 hours into minutes. Calculate the final distance covered in 4 hours using the corrected proportion.
    OR
    For the mid-day meal in a school with 120 students, the cook usually makes 15 kg of rice. On a rainy day, only 80 students came to school. How many kilograms of rice should the cook make so that the food is not wasted?

23. Fill in the blanks:
    (i) 3 is ___ % of 300 (ii) ___ is 40% of 4 (iii) 40 is 80% of ___

24. In one corner of the garden, there is a triangular flower bed. Its base is 6 m and its corresponding height is 4 m. If the school decided to double the base of this triangle to 12 m, while keeping the height the same, how would the area change?
    OR
    Give a method to obtain a rectangle whose area is twice that of a given triangle. What are the different methods that you can think of?

25. A total of ₹4,500 needs to be divided into two parts in the ratio 2:3. Determine the exact value of each of the two parts.

SECTION D (4 marks each)

26. Kishanlal recently opened a garment shop. He aims to achieve a daily sales of at least ₹5000. The sales on the first 2 days were ₹2000 and ₹3500. What percentage of his target did he achieve?

27. Verify if the triple (8, 15, 17) satisfies the Baudhāyana-Pythagoras theorem. Show all your calculations for a², b², and c².
    OR
    Find the side length of a rhombus whose diagonals are of length 24 units and 70 units.

28. Find the area of the shaded region given that ABCD is a rectangle. (diagram with dimensions)

SECTION E (Case-Based - 4 marks each)

29. The School Library Project: The students of Class 8 found that the library has a total of 800 books. Upon categorization: (i) 40% of the books are Storybooks (ii) 1/4 of the total books are Science and Mathematics books (iii) The remaining books are Biography and General Knowledge.
    (a) How many Storybooks are there in the library?
    (b) Find the total number of Science and Mathematics books, and express this amount as a percentage of the total books in the library.
    (c) If 20% of the Biography and General Knowledge books are donated to a local primary school, how many books are donated?

30. A rectangular garden has length (x + 8) meters and breadth (x - 2) meters. If both the length and breadth are increased by 1 meter:
    (a) Find the area of the original rectangular garden.
    (b) What is the area of the current rectangular garden after increase of 1 m?
    (c) How much area increased?

SAMPLE Paper 11 – Complete Solutions with Explanations

(Assuming the next paper in sequence is Paper 11, though it may be labeled differently in the PDF. I’ll proceed with the remaining content.)

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Section A – MCQs with Explanations

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Q1: Digital root of 489710?
a) 1 b) 2 c) 9 d) 11
✅ Answer: c) 9
Explanation: 4+8+9+7+1+0=29 → 2+9=11 → 1+1=2. Wait, recalc:
Sum=4+8=12, +9=21, +7=28, +1=29, +0=29 → 2+9=11 → 1+1=2. So digital root=2.
But option b) is 2, c) is 9.
Check: 489710 ÷ 9 remainder? Sum=29, 29÷9=3 remainder 2 → digital root=2. ✅ Answer: b) 2.

Q2: Number divisible by 9 if and only if:
A) Units digit 0 or 9 B) Even number C) Sum of digits divisible by 9 D) Divisible by 11
✅ Answer: C) Sum of digits divisible by 9.

Q3: Expand (a+m)(b+n):
a) ab+mn b) ab+mb+an+mn c) ab+an+m d) am+bn+ab
✅ Answer: b) ab+mb+an+mn

Q4: “Multiplication by parts” using distributive property is called in Brahmagupta’s work:
a) Ista-gunana b) Khanda-gunanam c) Ganita Prakash d) Brahmashputasiddhanta
✅ Answer: b) Khanda-gunanam.

Q5: Simplest form of 60:40:
a) 20:1 b) 3:2 c) 1.5:1 d) 6:4
✅ Answer: b) 3:2
Explanation: Divide by 20 → 3:2.

Q6: Two ratios a:b and c:d proportional (::) if:
a) a+d=b+c b) ad=bc c) a=c and b=d d) Terms are even
✅ Answer: b) ad=bc

Q7: Decimal equivalent of 40%:
a) 4.0 b) 0.04 c) 0.4 d) 0.44
✅ Answer: c) 0.4

Q8: Simplest form of 36/48:
a) 6/8 b) ¾ c) 3.099 d) 3.909
✅ Answer: b) ¾

Q9: Pythagorean triple:
a) (1,2,3) b) (5,12,13) c) (2,3,4) d) (7,8,10)
✅ Answer: b) (5,12,13)

Q10: √2 has property:
a) Terminating decimal b) Expressible as m/n with m,n positive integers c) Between 1.414 and 1.415, non-terminating d) Equal to 1.5
✅ Answer: c)

Q11: Parallelogram base 10 cm, height 6 cm → area:
a) 16 cm² b) 32 cm² c) 60 cm² d) 30 cm²
✅ Answer: c) 60 cm²
Explanation: 10×6=60.

Q12: Standard unit of area:
a) metre b) square metre c) centimetre d) kilogram
✅ Answer: b) square metre

Q13: Rhombus diagonals 10 cm and 24 cm → area:
a) 240 cm² b) 120 cm² c) 68 cm² d) 34 cm²
✅ Answer: b) 120 cm²
Explanation: ½×10×24=120.

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Assertion-Reason

Q14:
A: (x+3)(x+5)=x²+8x+15
R: Each term of first bracket multiplied with each term of second.
✅ Answer: (a) Both true, R explains A

Q15:
A: 15/20 = ¾
R: Equivalent fractions from multiplying/dividing numerator and denominator by same nonzero number.
✅ Answer: (a) Both true, R explains A
Explanation: 15/20 ÷ 5/5 = ¾.

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Section B – Short Answers (2 marks)

Q16: If a number divisible by 12, why must it be divisible by 3 and 4?
✅ Explanation: 12=3×4, and 3 and 4 are coprime → divisibility by 12 implies by both 3 and 4.

Q17: Digital root of 320185:
Sum=3+2+0+1+8+5=19 → 1+9=10 → 1+0=1.

Q18: Using distributive property: 94×11 = 94×(10+1)=940+94=1034.
OR ab when a,b increased by 1: (a+1)(b+1)=ab+a+b+1.

Q19: 50% of 8 = 0.5×8=4.
OR 15 of 80 students walk → %=(15/80)×100=18.75%.

Q20: Isosceles right triangle equal sides=3 cm → hypotenuse=3√2 cm.

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Section C – Short Answers (3 marks)

Q21: Sum of four consecutive numbers=34 → numbers=7,8,9,10.
OR 31z5 divisible by 9 → sum=3+1+z+5=9+z divisible by 9 → z=0 or 9 → two answers possible.

Q22: Car travels 90 km in 150 min → speed=90/150=0.6 km/min. In 4h=240 min → distance=0.6×240=144 km.
OR Midday meal: 120 students→15 kg rice, 80 students→ (15/120)×80=10 kg.

Q23: Fill blanks:
(i) 3 is 1% of 300.
(ii) 1.6 is 40% of 4.
(iii) 40 is 80% of 50.

Q24: Triangle base 6 m, height 4 m → area=12 m². If base doubled to 12 m, height same → area=24 m² (doubles).
OR Rectangle with area twice triangle: Use triangle as half of rectangle with same base and height → double triangle area = base×height rectangle.

Q25: ₹4500 divided in ratio 2:3 → parts = (2/5)×4500=1800 and (3/5)×4500=2700.

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Section D – Long Answers (4 marks)

Q26: Kishanlal target ₹5000/day. Day1=₹2000 (40%), Day2=₹3500 (70%).
Achieved 40% and 70%.

Q27: Verify (8,15,17) Pythagorean: 8²+15²=64+225=289=17² ✔.
OR Side of rhombus diagonals 24 and 70 → side=√(12²+35²)=37 units.

Q28: Area of shaded region in rectangle → need diagram.

Section E – Case-Based Questions (4 marks each)

Q29. The School Library Project

Context:
Total books = 800

• 40% are Storybooks.

• 1/4 are Science and Mathematics books.

• The rest are Biography and General Knowledge.

Questions:

(a) How many Storybooks?
✅ Answer:
40% of 800 = $0.40\times 800=320$
So, 320 Storybooks.

(b) Total number of Science and Mathematics books, and as a percentage of total.
✅ Answer:
1/4 of 800 = $\frac{1}{4}\times 800=200$ books.
Percentage = $\frac{200}{800}\times 100=25\mathrm{\%}$.

(c) If 20% of Biography and General Knowledge books are donated, how many books are donated?
✅ Answer:
Remaining books = 800 − (320 + 200) = 280 (Biography + GK).
20% of 280 = $0.20\times 280=56$ books donated.

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Q30. Rectangular Garden Dimensions

Context:
Original garden:

• Length = $x+8$ meters

• Breadth = $x-2$ meters
  Both length and breadth increased by 1 meter.

Questions:

(a) Area of original garden:
✅ Answer:

$$\text{Area}=(x+8)(x-2)=x^2+6x-16{\text{m}}^2$$

(b) Area after increasing both dimensions by 1 m:
✅ Answer:
New length = $x+9$
New breadth = $x-1$

$$\text{New area}=(x+9)(x-1)=x^2+8x-9{\text{m}}^2$$

(c) Increase in area:
✅ Answer:

$$\text{Increase}=(x^2+8x-9)-(x^2+6x-16)=2x+7{\text{m}}^2$$

Class 8 SESSION ENDING EXAMINATION (2026) SAMPLE PAPER-10 WITH ANSWERS

 

SAMPLE PAPER 10

SECTION A (MCQ & ARQ)

1. The digital root of an 8-digit number is 5. What will be the digital root of 10 more than that number?
   a) 5 b) 6 c) 1 d) 8

2. The number which is divisible by 11 is:
   a) 1234 b) 93547 c) 358095 d) 601436

3. The number of students in classes A and B are in the ratio 4:5. If 8 students are shifted from class B to A, the ratio becomes 1:1. How many students were there in class B initially?
   a) 65 b) 72 c) 80 d) 90

4. Jeevana purchased a story book of 216 pages and completed 162 pages. What percentage of the book is to be completed?
   a) 10% b) 15% c) 60% d) 25%

5. Percentages are fractions with denominator:
   a) 100 b) 10 c) 1 d) 50

6. Find the diagonal of a square with side length 5 cm:
   a) 25 cm b) 5√2 cm c) 2√5 cm d) 20 cm

7. Choose a Baudhayana-Pythagoras triple:
   a) 3,4,6 b) 6,8,11 c) 5,12,14 d) 12,16,20

8. Find the area of unshaded triangular part of the given rectangle. (diagram)

9. Match the following:
   i) The area of a triangle a) ½ × product of diagonals
   ii) The area of a rhombus b) ½ × base × height
   iii) Area of parallelogram c) ½ × height × sum of parallel sides
   iv) Area of trapezium d) base × height

10. Which pair of ratios is NOT proportional?
    a) 18:27 and 4:6 b) 25:40 and 5:8 c) 21:35 and 3:5 d) 16:24 and 5:7

11. Choose the incorrect one:
    a) (a + b)² = a² + 2ab + b² b) (a - b)² = a² - 2ab + b²
    c) (a + b)(c - d) = ac + ad + bc + bd d) a² - b² = (a + b)(a - b)

12. Which of the following is an example of the distributive property of multiplication over addition?
    a) (a + b = b + a) b) [a(b + c) = ab + ac] c) [(a + b) + c = a + (b + c)] d) (ab = ba)

13. How many m² is a Km²?
    a) 1000000 b) 100000 c) 10000 d) 1000

Assertion-Reason:

14. Assertion: The square of an even number is always divisible by 4.
    Reason: Any even number can be written as 2.

15. Assertion: If the price of an article increases by 20% and then decreases by 20%, the final price remains the same as the original price.
    Reason: An increase and decrease by the same percentage always cancel each other.

SECTION B (VSA - 2 marks each)

16. Find four consecutive numbers whose sum is 94.

17. A sports coach buys 24 kits. Each kit has 2 pairs of shoes and 3 T-shirts. Each boy is given a pair of shoes and a T-shirt. In that afternoon the coach has distributed shoes & T-shirt to 20 boys. How much T-shirt are left?

18. A TV is bought at a price of ₹21,000. After 1 year, the value of the TV depreciates by 5%. Find the value of the TV after one year.

19. If a = 8 cm and b = 12 cm are the sides of a right triangle, find the length of hypotenuse.

20. If 3p7q8 is divisible by 6, list any two pairs of values for 'p' and 'q'.

SECTION C (SA - 3 marks each)

21. Explain the divisibility test for 11 using place value with an example.

22. Percentage calculations: (question incomplete in PDF)

23. Find the area of the shaded region given that ABCD is a rectangle. (diagram)

24. Find the side length of a rhombus whose diagonals are of 24 units and 70 units.

25. Simplify a) 72 : 108 (b) 20 : 30 (c) Check whether the two ratios are proportional.

SECTION D (LA - 4 marks each)

26. A shopkeeper has a set of (21 + x) pens and the cost of each pen is ₹(21 - x)
    a) What is the total cost all his pens?
    b) Find the cost pens in the above case if x = 4

27. A four days scout and guide camp were arranged by the school for class 8 students.
    i) The school arranged 6 buses to take 150 students to the camp. If 75 more students are joined, how many buses are required in all?
    ii) In the camp, they assigned some jobs to the students. 45 students complete a job in 20 minutes. How many minutes will 30 students take to complete the same job?

28. Find the area of an equilateral triangle with side length 6 units. (Hint: Show that an altitude bisects the opposite side. Use this to find the height)

SECTION E (Case study based)

29. There is a pentagonal shaped park in a colony as shown in the figure. Class VIII students Jyoti and Kavitha are playing in the park. While playing, they start discussing how to find the area of the park. Jyoti divides the pentagon into triangles, while Kavitha divides it into rectangles and triangles. Both of them calculate the area using their own methods.
    a) Find the area of the square part of the park.
    b) Find the area of one triangular part of the park.
    c) Which method do you find easier, and why?

30. In a Kendriya Vidyalaya, attendance of students of Primary as well as Secondary is recorded on 2nd February 2026. The data is given in a table.
    a) Find the percentage of the strength of primary students (Class I - V) in the KV.
    b) What is the percentage of students absent in total?
    c) Find the difference between the percentage of attendance of boys and girls of Class VIII on 2nd February 2026.

SAMPLE Paper 10 – Complete Solutions with Explanations

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Section A – MCQs with Explanations

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Q1: Digital root of 8-digit number is 5 → digital root of number + 10 = ?
a) 5 b) 6 c) 1 d) 8
✅ Answer: b) 6
Explanation: Adding 10 adds 1 to digital root (since 10 → 1+0=1). 5+1=6.

Q2: Which is divisible by 11?
a) 1234 b) 93547 c) 358095 d) 601436
✅ Answer: b) 93547
Explanation: Divisibility by 11: (9+5+7)−(3+4)=21−7=14 not multiple of 11? Check:
Actually (odd place sum) – (even place sum) = (9+5+7)−(3+4)=21−7=14 → not 0/11/22. Let’s verify:
93547: digits 9(odd),3(even),5(odd),4(even),7(odd). Sum odd=9+5+7=21, even=3+4=7, diff=14 not divisible by 11 → so not divisible.
Check 601436: (6+1+3)=10, (0+4+6)=10, diff=0 ✔ divisible.
So correct answer: d) 601436.

Q3: Students in A:B = 4:5. If 8 students shift from B to A → ratio becomes 1:1 → initial B?
a) 65 b) 72 c) 80 d) 90
✅ Answer: c) 80
Explanation: Let A=4x, B=5x. After shift: A=4x+8, B=5x−8 → (4x+8)/(5x−8)=1 → 4x+8=5x−8 → x=16 → B=5×16=80.

Q4: Book 216 pages, completed 162 → % left?
a) 10% b) 15% c) 60% d) 25%
✅ Answer: d) 25%
Explanation: Left = 216−162=54 pages → % = (54/216)×100=25%.

Q5: Percentages are fractions with denominator ___
a) 100 b) 10 c) 1 d) 50
✅ Answer: a) 100

Q6: Diagonal of square side 5 cm:
a) 25 cm b) 5√2 cm c) 2√5 cm d) 20 cm
✅ Answer: b) 5√2 cm

Q7: Pythagorean triple:
a) 3,4,6 b) 6,8,11 c) 5,12,14 d) 12,16,20
✅ Answer: d) 12,16,20
Explanation: 12²+16²=144+256=400=20².

Q8: Area of unshaded triangle in rectangle → need diagram.
Likely half of rectangle.

Q9: Match formulas:
i) Triangle area → ½×base×height
ii) Rhombus area → ½×product of diagonals
iii) Parallelogram area → base×height
iv) Trapezium area → ½×height×sum of parallel sides
✅ Answer: D) i-b, ii-a, iii-d, iv-c

Q10: Which ratio pair NOT proportional?
a) 18:27 & 4:6 (both 2:3) b) 25:40 & 5:8 (both 5:8) c) 21:35 & 3:5 (both 3:5) d) 16:24 & 5:7 (16:24=2:3, 5:7≠2:3)
✅ Answer: d) 16:24 & 5:7

Q11: Incorrect identity:
a) (a+b)² = a²+2ab+b² b) (a−b)² = a²−2ab+b² c) (a+b)(c−d) = ac+ad+bc+bd d) a²−b² = (a+b)(a−b)
✅ Answer: c) Should be ac−ad+bc−bd.

Q12: Distributive property example:
a) a+b=b+a b) a(b+c)=ab+ac c) (a+b)+c=a+(b+c) d) ab=ba
✅ Answer: b)

Q13: How many m² in 1 km²?
a) 1,000,000 b) 100,000 c) 10,000 d) 1000
✅ Answer: a) 1,000,000

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Assertion-Reason

Q14:
A: Square of even number divisible by 4.
R: Any even number can be written as 2.
✅ Answer: (c) A true, R false
Explanation: R incomplete (should be 2k).

Q15:
A: Price increases 20% then decreases 20% → same as original.
R: Increase and decrease by same % cancel.
✅ Answer: (d) A false, R false
Explanation: They don’t cancel multiplicatively.

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Section B – Short Answers (2 marks)

Q16: Four consecutive numbers sum to 94 → find them.
✅ Answer: Let numbers: n, n+1, n+2, n+3 → 4n+6=94 → 4n=88 → n=22 → numbers: 22,23,24,25.

Q17: Coach buys 24 kits, each: 2 shoes + 3 T-shirts. Distributes to 20 boys (1 shoe+1 T-shirt each). T-shirts left?
✅ Explanation: Total T-shirts = 24×3=72. Used = 20×1=20 → left=52.
But careful: Shoes per boy=1, T-shirts per boy=1. Yes, so T-shirts used=20 → left=72−20=52.

Q18: TV ₹21,000, depreciates 5% after 1 year → value = 21000×0.95=₹19,950.

Q19: Right triangle sides a=8 cm, b=12 cm → hypotenuse = √(8²+12²)=√(64+144)=√208=4√13 cm.

Q20: 3p7q8 divisible by 6 → find two pairs for p,q.
✅ Explanation: Divisible by 6 → divisible by 2 and 3.

• By 2: last digit 8 even ✔

• By 3: sum digits=3+p+7+q+8=18+p+q divisible by 3 → p+q divisible by 3.
  Pick p=1,q=2 (sum=3) → 31728.
  p=2,q=1 → 32718.

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Section C – Short Answers (3 marks)

Q21: Divisibility test for 11 using place value:
Odd-position digits sum − Even-position digits sum = 0 or multiple of 11.
Example: 121: (1+1)−2=0 ✔ divisible.

Q22: Not fully stated, likely percentage calculations.

Q23: Area of shaded region in rectangle → need diagram.

Q24: Side of rhombus diagonals 24 and 70 → side=√(12²+35²)=√1369=37 units.

Q25: Simplify ratios:
a) 72:108 = 2:3 b) 20:30=2:3
c) Proportional? Yes, both 2:3.

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Section D – Long Answers (4 marks)

Q26: Shopkeeper pens: (21+x) pens, each cost ₹(21−x) → total cost = (21+x)(21−x)=441−x².
If x=4 → total=441−16=425.

Q27: Scout camp:
(i) 6 buses for 150 students → 1 bus=25 students. If 75 more join → total=225 → buses=225/25=9.
(ii) 45 students → 20 min, 30 students → time inversely proportional → (45/30)×20=30 min.

Q28: Equilateral triangle side 6 units → height = 3√3 → area = ½×6×3√3=9√3 units².

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Section E – Case-Based (4 marks)

Q29: Pentagonal park:
a) Square part area = side² (need dimensions).
b) Triangular part area = ½×base×height.
c) Easier method depends on division.

Q30: KV attendance table:
a) Primary (I–V) total strength = 777 → % of total 1537 = (777/1537)×100≈50.55%.
b) Total absent = Total strength − Total present = 1537−1351=186 → % absent = (186/1537)×100≈12.1%.
c) Class VIII: Boys present=74, total boys=82 → % boys present=90.24%. Girls present=65, total girls=76 → % girls present=85.53%. Difference ≈ 4.71%.