Case Study Questions Class 10 Maths: Chapter-Wise with Solutions
One real-life case study for every CBSE Class 10 Maths chapter, each with four linked questions and worked solutions, plus tips to solve case questions fast.
Case study questions in Class 10 Maths give a short real-life situation, such as a garden, a savings plan or a lighthouse, followed by three or four linked questions. Read the case once, write down the given values, identify the chapter's formula, then answer each part in order. Below is one case study for each of the 14 chapters, with worked solutions.
Case study questions now make up a big part of the CBSE Class 10 Maths paper. Many students lose marks not because the maths is hard, but because they get lost in the story. This page gives you one case study for every chapter, each with four linked questions and full solutions, so you can practise picking out the numbers and the right formula quickly. All cases are original and follow the current rationalised NCERT syllabus.
How to solve a case study question
- Read the case once and underline every number with its unit.
- Skim all the sub-questions to see what you will need.
- Name the chapter and formula before calculating.
- Answer in order, using earlier answers where they help.
- Check units and whether the answer makes sense in the story.
Chapter 1: Real Numbers
Case: A sports teacher wants to arrange 36 boys and 60 girls in rows for a drill. Every row must have the same number of students, and each row must have only boys or only girls.
- What is the greatest number of students possible in each row?
- How many rows will there be in total?
- Write the prime factorisation of 60.
- Find LCM(36, 60).
Show solutions
(i) HCF(36, 60) = 12 students per row. (ii) 36 ÷ 12 + 60 ÷ 12 = 3 + 5 = 8 rows. (iii) 60 = 2² × 3 × 5. (iv) 36 = 2² × 3², so LCM = 2² × 3² × 5 = 180.
Chapter 2: Polynomials
Case: The height of a water jet from a fountain, in metres, is given by p(x) = −x² + 4x, where x is the horizontal distance in metres from the nozzle.
- Find the zeroes of p(x).
- How far from the nozzle does the water land?
- Verify the relationship between the zeroes and the coefficients.
- Does the graph of p(x) open upwards or downwards? Why?
Show solutions
(i) −x² + 4x = −x(x − 4) = 0, so x = 0 or x = 4. (ii) 4 m from the nozzle. (iii) Sum = 0 + 4 = 4 = −b/a = −4/(−1); product = 0 = c/a = 0/(−1). (iv) Downwards, because the coefficient of x² is negative.
Chapter 3: Pair of Linear Equations in Two Variables
Case: At a stationery shop, 2 pencils and 3 erasers cost ₹26, while 3 pencils and 2 erasers cost ₹24.
- Write the pair of linear equations, taking the cost of a pencil as ₹p and an eraser as ₹e.
- Find p + e.
- Find the cost of one pencil and one eraser.
- What is the cost of 5 pencils and 4 erasers?
Show solutions
(i) 2p + 3e = 26 and 3p + 2e = 24. (ii) Adding: 5p + 5e = 50, so p + e = 10. (iii) Subtracting the first from the second: p − e = −2. So p = 4 and e = 6: a pencil costs ₹4 and an eraser ₹6. (iv) 5(4) + 4(6) = ₹44.
Chapter 4: Quadratic Equations
Case: A rectangular kitchen garden is 3 m longer than it is wide. Its area is 70 m².
- Form a quadratic equation, taking the breadth as b metres.
- Find the length and breadth.
- Find the perimeter of the garden.
- Find the discriminant and state the nature of the roots.
Show solutions
(i) b(b + 3) = 70, so b² + 3b − 70 = 0. (ii) (b + 10)(b − 7) = 0, so b = 7 (a length cannot be −10). Breadth 7 m, length 10 m. (iii) 2(10 + 7) = 34 m. (iv) D = 3² − 4(1)(−70) = 9 + 280 = 289 > 0, so two distinct real roots.
Chapter 5: Arithmetic Progressions
Case: Riya saves ₹50 in the first week of the year and increases her savings by ₹20 every week.
- What is the common difference?
- How much does she save in the 10th week?
- How much has she saved in total after 10 weeks?
- In which week does she save ₹410?
Show solutions
(i) d = ₹20. (ii) a₁₀ = 50 + 9 × 20 = ₹230. (iii) S₁₀ = 10/2 × (50 + 230) = 5 × 280 = ₹1,400. (iv) 50 + (n − 1)20 = 410 gives n − 1 = 18, so the 19th week.
Chapter 6: Triangles
Case: At 4 p.m., a 1.5 m tall girl casts a shadow 2 m long. At the same time, a vertical pole casts a shadow 12 m long.
- Why are the two triangles formed by the girl and the pole with their shadows similar?
- Find the height of the pole.
- Later, the girl's shadow is 3 m long. How long is the pole's shadow then?
- State the similarity criterion used.
Show solutions
(i) Both stand vertically (right angle at the ground) and the sun's rays make the same angle with the ground. (ii) h/12 = 1.5/2, so h = 9 m. (iii) The ratio height : shadow is the same for both, so pole's shadow = 12 × 3/2 = 18 m. (iv) AA similarity.
Chapter 7: Coordinate Geometry
Case: On a village map drawn on a grid, the school is at A(2, 3), the library at B(6, 6) and the park at C(10, 3).
- Find the distance between the school and the library.
- Find the midpoint of the school and the park.
- Show that triangle ABC is isosceles.
- Find the point that divides AC in the ratio 1 : 3.
Show solutions
(i) AB = √[(6 − 2)² + (6 − 3)²] = √(16 + 9) = 5 units. (ii) ((2 + 10)/2, (3 + 3)/2) = (6, 3). (iii) BC = √[(10 − 6)² + (3 − 6)²] = √(16 + 9) = 5 = AB, so ABC is isosceles. (iv) x = (1 × 10 + 3 × 2)/4 = 4, y = (1 × 3 + 3 × 3)/4 = 3, so (4, 3).
Chapter 8: Introduction to Trigonometry
Case: A wheelchair ramp rises 5 m over a horizontal distance of 12 m. The sloping surface is 13 m long. Let θ be the angle the ramp makes with the ground.
- Find sin θ, cos θ and tan θ.
- Verify that sin²θ + cos²θ = 1.
- Find sec θ.
- If another ramp has tan θ = 1, what is θ?
Show solutions
(i) sin θ = 5/13, cos θ = 12/13, tan θ = 5/12. (ii) 25/169 + 144/169 = 169/169 = 1. (iii) sec θ = 1/cos θ = 13/12. (iv) θ = 45°.
Chapter 9: Some Applications of Trigonometry
Case: From the top of a 30 m tall lighthouse, the angle of depression of a boat is 30°. Later, as the boat sails towards the lighthouse, the angle becomes 60°. (Take √3 ≈ 1.732.)
- What is the angle of elevation of the top of the lighthouse from the boat's first position?
- How far is the boat from the foot of the lighthouse at first?
- How far is it at the second position?
- How far did the boat travel?
Show solutions
(i) 30° (equal to the angle of depression). (ii) tan 30° = 30/d, so d = 30√3 ≈ 51.96 m. (iii) tan 60° = 30/d, so d = 30/√3 = 10√3 ≈ 17.32 m. (iv) 30√3 − 10√3 = 20√3 ≈ 34.64 m.
Chapter 10: Circles
Case: A circular running track has a radius of 5 m. A lamp post P stands 13 m from the centre O. Two straight paths from P just touch the track at A and B.
- What is the angle between OA and the path PA?
- Find the length of the path PA.
- How long is PB?
- How many such paths could be drawn from a point on the track itself?
Show solutions
(i) 90°, because a tangent is perpendicular to the radius at the point of contact. (ii) PA = √(13² − 5²) = √144 = 12 m. (iii) 12 m: tangents from an external point are equal. (iv) Exactly one.
Chapter 11: Areas Related to Circles
Case: A round pizza of radius 14 cm is cut into 8 equal slices. (Take π = 22/7.)
- What is the angle at the centre of each slice?
- Find the area of one slice.
- Find the length of crust on one slice.
- Find the perimeter of one slice.
Show solutions
(i) 360° ÷ 8 = 45°. (ii) (45/360) × (22/7) × 14² = (1/8) × 616 = 77 cm². (iii) (1/8) × 2 × (22/7) × 14 = (1/8) × 88 = 11 cm. (iv) 14 + 14 + 11 = 39 cm.
Chapter 12: Surface Areas and Volumes
Case: A juice can is a closed cylinder with radius 3.5 cm and height 10 cm. (Take π = 22/7.)
- Find the volume of the can.
- How much juice, in millilitres, can it hold?
- Find the area of the label that wraps around the curved surface.
- Find the total surface area of the can.
Show solutions
(i) πr²h = (22/7) × 3.5 × 3.5 × 10 = 385 cm³. (ii) 385 ml, since 1 cm³ = 1 ml. (iii) 2πrh = 2 × (22/7) × 3.5 × 10 = 220 cm². (iv) 2πr(h + r) = 2 × (22/7) × 3.5 × 13.5 = 297 cm².
Chapter 13: Statistics
Case: The marks (out of 50) of 30 students are grouped as: 0-10: 3 students, 10-20: 5, 20-30: 10, 30-40: 8, 40-50: 4.
- Find the modal class and the mode.
- Find the median class.
- Find the median.
- Find the mean, using class marks.
Show solutions
(i) Modal class 20-30. Mode = 20 + [(10 − 5)/(2 × 10 − 5 − 8)] × 10 = 20 + (5/7) × 10 ≈ 27.14. (ii) n/2 = 15; cumulative frequencies 3, 8, 18, so the median class is 20-30. (iii) Median = 20 + [(15 − 8)/10] × 10 = 27. (iv) Σfx = 5×3 + 15×5 + 25×10 + 35×8 + 45×4 = 800, so mean = 800/30 ≈ 26.67.
Chapter 14: Probability
Case: A bag has 5 red, 3 blue and 2 green balls of the same size. One ball is drawn at random.
- Find P(red).
- Find P(not blue).
- Find P(green or blue).
- Find P(yellow).
Show solutions
(i) 5/10 = 1/2. (ii) 7/10. (iii) 5/10 = 1/2. (iv) 0: there are no yellow balls, so it is an impossible event.
How to get full marks on case studies
- Write the formula first, then substitute. Steps earn marks even if the final answer slips.
- Reject impossible answers such as a negative length, and say why.
- Practise the official style in CBSE's 2025-26 Class 10 sample papers and the NCERT Exemplar problems.
- Match the syllabus: check chapters against the current CBSE curriculum.
For quick 1-mark practice, try our assertion-reason questions for Class 10 Maths, and read what competency-based questions are. Our guide on how to get good marks in Class 10 Maths covers the whole paper. On Intellicamp, chapter-wise tests include case-based questions among 24 question types, with instant marking and your weak topics shown. See how it works for students.
- Underline the numbers, skim the sub-questions, then name the formula.
- Later parts often use earlier answers; work in order.
- Show steps and check units for every part.
Frequently asked questions
How many marks are case study questions in Class 10 Maths?
In recent CBSE papers, case-based questions are usually 4 marks each, split across sub-parts. Check the latest sample paper on cbseacademic.nic.in for the exact pattern.
Are case study questions harder than normal questions?
Not usually. The maths is the same as the chapter's normal questions; the difference is that you must pick out the numbers from a story. Practice makes this quick.
Should I read all sub-questions before starting?
Yes. Later parts often build on earlier ones, so a quick look shows what you will need to calculate.
Do these follow the rationalised syllabus?
Yes. They cover the 14 chapters of the current NCERT Class 10 Mathematics book and avoid deleted topics such as frustums and the area of a triangle in coordinate geometry.
Where can I practise more case-based questions?
CBSE sample papers and NCERT Exemplar problems have more. Intellicamp's chapter-wise tests also include case-based questions, marked instantly.
Practise this chapter free
Take a short practice test on any chapter, get it marked instantly, and see exactly which topics are costing you marks.