CBSE Class 9 Mathematics Mathematical Modelling MCQs Set 17

Download CBSE MCQs for Class 9 Mathematics: Mathematical Modelling

Access targeted multiple-choice questions for Mathematical Modelling designed to align with the latest CBSE academic syllabus for Class 9 Mathematics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

Chapter-wise Objective Questions: Mathematical Modelling

Navigate directly to the 50 objective questions for Mathematical Modelling using the digital viewer below. Each practice set includes verified answer keys, allowing students to instantly cross-check their work and identify areas requiring further revision.

Multiple Choice Questions

Question 1: A model describing a real-life situation by a mathematical relation is called a
(a) mathematical model
(b) conjecture
(c) theorem
(d) axiom
Show Answer & Explanation

Answer: (a) mathematical model

Explanation:
1. A mathematical model is a relation or set of equations describing a real situation.
2. Example: area of an equilateral triangle = (√3/4) × side².

Teacher's Note:
1. Models are tools to solve real-life problems.

Question 2: The correct order of the steps of mathematical modelling is
(a) solution, formulation, validation, interpretation
(b) formulation, solution, interpretation, validation
(c) interpretation, formulation, solution, validation
(d) formulation, validation, solution, interpretation
Show Answer & Explanation

Answer: (b) formulation, solution, interpretation, validation

Explanation:
1. First state the problem and form the equations (formulation), then solve, then interpret in the real situation, then check validity.

Teacher's Note:
1. Validation checks whether the result fits reality.

Question 3: A car travels 416 km on 52 litres of petrol. The petrol needed for 96 km is
(a) 10 litres
(b) 14 litres
(c) 12 litres
(d) 8 litres
Show Answer & Explanation

Answer: (c) 12 litres

Explanation:
1. Petrol is directly proportional to distance: y = kx with k = 52/416 = 1/8.
2. y = 96 × 1/8 = 12 litres.

Teacher's Note:
1. Assumes mileage stays the same.

Question 4: The result in the petrol problem (12 litres for 96 km) is valid only if
(a) the car is new
(b) the petrol price is constant
(c) the distance is a whole number
(d) the mileage and road conditions remain the same
Show Answer & Explanation

Answer: (d) the mileage and road conditions remain the same

Explanation:
1. The model assumes a constant ratio of petrol to distance (same car, same road, same speed).

Teacher's Note:
1. Assumptions are part of validation.

Question 5: Rakesh invests Rs. 20,000 at 12% simple interest per year to buy a TV costing Rs. 25,000 from the interest plus the principal. The number of years needed is
(a) 2 years 1 month
(b) 2 years
(c) 2 years 6 months
(d) 2 years 3 months
Show Answer & Explanation

Answer: (a) 2 years 1 month

Explanation:
1. Interest needed = 5000. S.I. = 20000 × 12 × n / 100 = 2400n.
2. 2400n = 5000 gives n = 25/12 years = 2 years 1 month.

Teacher's Note:
1. 1/12 of a year is one month.

Question 6: A motor boat takes 8 hours upstream and 5 hours downstream between two towns. The speed of the stream is 4 km/h. The speed of the boat in still water is
(a) 16 km/h
(b) 52/3 km/h
(c) 20 km/h
(d) 40/3 km/h
Show Answer & Explanation

Answer: (b) 52/3 km/h

Explanation:
1. Let the boat speed be x: distance = 8(x − 4) = 5(x + 4).
2. 8x − 32 = 5x + 20 gives x = 52/3 ≈ 17.33 km/h.

Teacher's Note:
1. Upstream speed is x − 4 and downstream speed is x + 4.

Question 7: For the same motor boat (still-water speed 52/3 km/h, 8 hours upstream, stream 4 km/h), the distance between the two towns is nearly
(a) 96 km
(b) 120 km
(c) 106.67 km
(d) 86.67 km
Show Answer & Explanation

Answer: (c) 106.67 km

Explanation:
1. Distance = 8 × (52/3 − 4) = 8 × 40/3 = 320/3 ≈ 106.67 km.

Teacher's Note:
1. Check with downstream: 5 × (52/3 + 4) = 5 × 64/3 = 106.67.

Question 8: 400 tickets were sold at Rs. 20 for adults and Rs. 10 for students and Rs. 6000 was collected. The number of adults was
(a) 100
(b) 150
(c) 250
(d) 200
Show Answer & Explanation

Answer: (d) 200

Explanation:
1. Let adults = x: 20x + 10(400 − x) = 6000.
2. 10x = 2000, so x = 200.

Teacher's Note:
1. Check: 200 × 20 + 200 × 10 = 6000.

Question 9: The price of sugar rises by 40%. To keep the expenditure the same, the consumption must be reduced by nearly
(a) 28.57%
(b) 40%
(c) 25%
(d) 35%
Show Answer & Explanation

Answer: (a) 28.57%

Explanation:
1. Rs. 100 buys x kg earlier; now Rs. 100 buys 100x/140 = 5x/7 kg.
2. Reduction = 2x/7 of the original, i.e. 28 4/7 %.

Teacher's Note:
1. Reduction is 40/140, not 40/100.

Question 10: A company can hire a computer at Rs. 2000 per month or buy it for Rs. 25000. Buying is cheaper if it is needed for at least
(a) 12 months
(b) 13 months
(c) 12.5 months
(d) 14 months
Show Answer & Explanation

Answer: (b) 13 months

Explanation:
1. Buying is cheaper when 25000 < 2000x, i.e. x > 12.5.
2. The least whole number of months is 13.

Teacher's Note:
1. 12 months costs Rs. 24000, which is less than 25000.

Question 11: Gold medal timings in the 400 m Olympic race are modelled by the formula T = 52.01 − 0.26n, with n = 0 for 1964 and one step per Olympic. The estimated timing for n = 11 is
(a) 50.00 seconds
(b) 48.00 seconds
(c) 49.15 seconds
(d) 52.01 seconds
Show Answer & Explanation

Answer: (c) 49.15 seconds

Explanation:
1. T = 52.01 − 0.26 × 11 = 52.01 − 2.86 = 49.15 seconds.

Teacher's Note:
1. Such a model is only an estimate.

Question 12: A sailor rows 8 km downstream in 40 minutes and returns in 1 hour. The speed of the sailor in still water is
(a) 12 km/h
(b) 8 km/h
(c) 2 km/h
(d) 10 km/h
Show Answer & Explanation

Answer: (d) 10 km/h

Explanation:
1. Downstream speed = 8 ÷ (2/3) = 12 km/h; upstream speed = 8 km/h.
2. Still-water speed = (12 + 8) ÷ 2 = 10 km/h.

Teacher's Note:
1. Boat speed is the mean of the two speeds.

Question 13: For the same sailor (12 km/h downstream, 8 km/h upstream), the speed of the current is
(a) 2 km/h
(b) 4 km/h
(c) 10 km/h
(d) 20 km/h
Show Answer & Explanation

Answer: (a) 2 km/h

Explanation:
1. Current = (12 − 8) ÷ 2 = 2 km/h.

Teacher's Note:
1. Half the difference of the two speeds.

Question 14: Ajeet takes 2 hours more than Amit to cover 30 km. If Ajeet doubled his speed he would take 1 hour less than Amit. Ajeet's speed is
(a) 7.5 km/h
(b) 5 km/h
(c) 6 km/h
(d) 10 km/h
Show Answer & Explanation

Answer: (b) 5 km/h

Explanation:
1. 30/a − 30/b = 2 and 15/a = 30/b − 1. Eliminating 15/a: 1 + 15/b = 30/b − 1 gives b = 7.5.
2. Then 30/a = 2 + 4 = 6, so a = 5 km/h.

Teacher's Note:
1. Amit's speed is 7.5 km/h.

Question 15: Two cars start from places 80 km apart, travelling at different speeds. They meet in 8 hours if moving in the same direction and in 1 hour 20 minutes if moving towards each other. The speeds are
(a) 30 km/h and 30 km/h
(b) 40 km/h and 20 km/h
(c) 35 km/h and 25 km/h
(d) 45 km/h and 15 km/h
Show Answer & Explanation

Answer: (c) 35 km/h and 25 km/h

Explanation:
1. Same direction: x − y = 80 ÷ 8 = 10.
2. Opposite: x + y = 80 ÷ (4/3) = 60. So x = 35 and y = 25.

Teacher's Note:
1. Relative speed: difference or sum.

Question 16: A bag has Rs. 1, 50 paise and 25 paise coins in the ratio 5 : 6 : 7 with total value Rs. 390. The number of 50 paise coins is
(a) 200
(b) 280
(c) 300
(d) 240
Show Answer & Explanation

Answer: (d) 240

Explanation:
1. Let the numbers be 5x, 6x, 7x. Value = 5x + 3x + 1.75x = 9.75x = 390, so x = 40.
2. 50 paise coins = 6 × 40 = 240.

Teacher's Note:
1. Convert paise into rupees.

Question 17: The ages of two persons are in the ratio 5 : 7. Sixteen years ago the ratio was 3 : 5. Their present ages are
(a) 40 and 56 years
(b) 30 and 42 years
(c) 35 and 49 years
(d) 45 and 63 years
Show Answer & Explanation

Answer: (a) 40 and 56 years

Explanation:
1. Let ages be 5x and 7x: (5x − 16) : (7x − 16) = 3 : 5.
2. 25x − 80 = 21x − 48 gives x = 8, so 40 and 56.

Teacher's Note:
1. Cross-multiply the ratio.

Question 18: Sudhir invests Rs. 15,000 at 8% simple interest per year to buy a Rs. 19,000 washing machine from the principal plus interest. The time needed is
(a) 3 years
(b) 3 years 4 months
(c) 3 years 6 months
(d) 4 years
Show Answer & Explanation

Answer: (b) 3 years 4 months

Explanation:
1. Interest needed = 4000. S.I. per year = 1200.
2. n = 4000 ÷ 1200 = 10/3 years = 3 years 4 months.

Teacher's Note:
1. 1/3 year = 4 months.

Question 19: A motorboat covers the distance between two points in 6 hours upstream and 5 hours downstream. The stream speed is 2 km/h. The speed of the boat in still water is
(a) 20 km/h
(b) 24 km/h
(c) 22 km/h
(d) 12 km/h
Show Answer & Explanation

Answer: (c) 22 km/h

Explanation:
1. 6(x − 2) = 5(x + 2).
2. 6x − 12 = 5x + 10 gives x = 22 km/h.

Teacher's Note:
1. Distance is the same both ways.

Question 20: The floor of a room is 6 m by 5 m and is covered with square tiles of side 30 cm laid in rows without cutting, a partial tile counting as a whole tile. The number of tiles needed is
(a) 334
(b) 333
(c) 360
(d) 340
Show Answer & Explanation

Answer: (d) 340

Explanation:
1. Along 6 m: 600 ÷ 30 = 20 tiles. Along 5 m: 500 ÷ 30 = 16.67, so 17 tiles.
2. Tiles = 20 × 17 = 340.

Teacher's Note:
1. By area alone the answer would be about 333.3, but rows of whole tiles need 340.

Question 21: A car goes 432 km on 48 litres of petrol. The petrol needed for 180 km is
(a) 20 litres
(b) 15 litres
(c) 25 litres
(d) 18 litres
Show Answer & Explanation

Answer: (a) 20 litres

Explanation:
1. 432 ÷ 48 = 9 km per litre.
2. 180 ÷ 9 = 20 litres.

Teacher's Note:
1. Direct proportion.

Question 22: A car from Delhi at 70 km/h and a motorcycle from Chandigarh at 55 km/h start towards each other at the same time. The distance is 250 km. They meet after
(a) 2.5 hours
(b) 2 hours
(c) 3 hours
(d) 1.5 hours
Show Answer & Explanation

Answer: (b) 2 hours

Explanation:
1. Closing speed = 70 + 55 = 125 km/h.
2. Time = 250 ÷ 125 = 2 hours.

Teacher's Note:
1. Speeds add when moving towards each other.

Free study material for Mathematics

Mathematical Modelling Objective Questions & Solutions for Class 9 Mathematics

Download Multiple Choice Questions: Mathematical Modelling (Class 9 Mathematics)

Explore reliable practice questions for Mathematical Modelling tailored for Class 9 Mathematics learners. Use these multiple-choice formats to evaluate preparedness and strengthen problem-solving skills.

Concept Clarification for Mathematical Modelling

Cross-reference your completed choices with comprehensive NCERT solutions for Class 9 Mathematics to ensure absolute clarity across all sub-topics in this chapter.

Additional Study Resources for Class 9 Mathematics

Explore our broader library of printable assignments, chapter notes, and mock tests designed to support continuous revision and secure higher marks in CBSE assessments.

FAQs

Where can I access latest CBSE Class 9 Mathematics Mathematical Modelling MCQs Set 17?

You can get most exhaustive CBSE Class 9 Mathematics Mathematical Modelling MCQs Set 17 for free on StudiesToday.com. These MCQs for Class 9 Mathematics are updated for the 2026-27 academic session as per CBSE examination standards.

Are Assertion-Reasoning and Case-Study MCQs included in the Mathematics Class 9 material?

Yes, our CBSE Class 9 Mathematics Mathematical Modelling MCQs Set 17 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the CBSE paper is now competency-based.

How do practicing Mathematics MCQs help in scoring full marks in Class 9 exams?

By solving our CBSE Class 9 Mathematics Mathematical Modelling MCQs Set 17, Class 9 students can improve their accuracy and speed which is important as objective questions provide a chance to secure 100% marks in the Mathematics.

Do you provide answers and explanations for CBSE Class 9 Mathematics Mathematical Modelling MCQs Set 17?

Yes, Mathematics MCQs for Class 9 have answer key and brief explanations to help students understand logic behind the correct option as its important for 2026 competency-focused CBSE exams.

Can I practice these Mathematics Class 9 MCQs online?

Yes, you can also access online interactive tests for CBSE Class 9 Mathematics Mathematical Modelling MCQs Set 17 on StudiesToday.com as they provide instant answers and score to help you track your progress in Mathematics.