Chapter 3 of 14
Chapter 3: A Trip to Bhopal
Excursion Planning, Bus Seating, Petrol Pumps, Narmada Bridge & Bhimbetka Time Math | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- Calculating bus requirements based on total students and seat capacities (50-seater vs 35-seater mini-buses).
- Bridge length, river water level differences, and speed calculations over the Narmada River.
- Fuel costs, diesel filling rates, and time taken at petrol pumps.
- Prehistoric cave paintings at Bhimbetka: counting animal and human figures; boat ride ticket budgeting at Upper Lake Bhopal.
All Textbook Exercises & In-Text Tasks (15 Questions)
100% Complete Ingestion
Q1
Excursion Bus Seating Calculation
Total students going on the Bhopal trip from Class 1 to Class 5 are: Class 1: 33, Class 2: 32, Class 3: 42, Class 4: 50, Class 5: 53. (a) How many total children are going on the trip? (b) If the school hires 4 buses with 50 seats each, how many children will get seats? (c) How many children will be left without seats?
[3 Marks]
✅ Step-by-Step Solution & Working
(a) Total Children Going on the Trip:
33 (Class 1)
+ 32 (Class 2)
+ 42 (Class 3)
+ 50 (Class 4)
+ 53 (Class 5)
-------
210 total children.
(b) Seating Capacity of 4 Buses:
• Each bus has 50 seats.
• 4 buses have 4 × 50 = 200 seats.
So, 200 children will get seats.
(c) Children Left Without Seats:
• 210 - 200 = 10 children will be left without seats.
(They will share seats with classmates).
33 (Class 1)
+ 32 (Class 2)
+ 42 (Class 3)
+ 50 (Class 4)
+ 53 (Class 5)
-------
210 total children.
(b) Seating Capacity of 4 Buses:
• Each bus has 50 seats.
• 4 buses have 4 × 50 = 200 seats.
So, 200 children will get seats.
(c) Children Left Without Seats:
• 210 - 200 = 10 children will be left without seats.
(They will share seats with classmates).
CBSE Step-by-Step Marking Scheme
Correct sum of 210 children
1.0 M
Correct calculation of 200 seats in 4 buses
1.0 M
Difference of 10 children without seats
1.0 M
Q2
Boat Ride Rates & Time Budgeting
At the Bhopal lake, ticket prices are: Double-Decker Boat: ₹30 (45 mins), Motor Boat: ₹25 (20 mins), Paddle Boat: ₹15 (30 mins), Oar Boat: ₹15 (45 mins). (a) Indra and Bhanu first took the motor boat and then the oar boat. How much total did they pay for both? (b) Which boat makes two trips in 1 hour?
[3 Marks]
✅ Step-by-Step Solution & Working
(a) Cost for Indra and Bhanu:
• Motor boat: Ticket = ₹25 per person. For 2 persons = 2 × ₹25 = ₹50.
• Oar boat: Ticket = ₹15 per person. For 2 persons = 2 × ₹15 = ₹30.
• Total amount paid = ₹50 + ₹30 = ₹80.
(b) Boat that makes 2 trips in 1 hour:
• 1 hour = 60 minutes.
• Time for 1 trip must be 60 ÷ 2 = 30 minutes.
• Looking at the table, the Paddle Boat has a trip duration of 30 minutes. Hence, the paddle boat makes two trips in 1 hour.
• Motor boat: Ticket = ₹25 per person. For 2 persons = 2 × ₹25 = ₹50.
• Oar boat: Ticket = ₹15 per person. For 2 persons = 2 × ₹15 = ₹30.
• Total amount paid = ₹50 + ₹30 = ₹80.
(b) Boat that makes 2 trips in 1 hour:
• 1 hour = 60 minutes.
• Time for 1 trip must be 60 ÷ 2 = 30 minutes.
• Looking at the table, the Paddle Boat has a trip duration of 30 minutes. Hence, the paddle boat makes two trips in 1 hour.
CBSE Step-by-Step Marking Scheme
Correct total fare of ₹80 for 2 children
1.5 M
Correct identification of Paddle Boat with 30 min duration
1.5 M
Q3
Travel Budget • Boating Rates
At the Bhopal lake, a motorboat charges ₹25 per person for a 20-minute ride, and a paddle boat charges ₹15 per person for a 45-minute ride. A group of 4 children have ₹100 and 40 minutes time. Which boat ride can they take?
[3 Marks]
✅ Step-by-Step Solution & Working
Comparison of Boating Options for 4 Children:
Available Budget = ₹100, Available Time = 40 minutes.
1. Motorboat Option:
• Total Cost = 4 × ₹25 = ₹100 (Within budget).
• Duration = 20 minutes (Well within 40 minutes).
2. Paddle Boat Option:
• Total Cost = 4 × ₹15 = ₹60 (Within budget).
• Duration = 45 minutes (Exceeds available 40 minutes).
Conclusion: They can only take the motorboat ride because the paddle boat exceeds their 40-minute time limit.
Available Budget = ₹100, Available Time = 40 minutes.
1. Motorboat Option:
• Total Cost = 4 × ₹25 = ₹100 (Within budget).
• Duration = 20 minutes (Well within 40 minutes).
2. Paddle Boat Option:
• Total Cost = 4 × ₹15 = ₹60 (Within budget).
• Duration = 45 minutes (Exceeds available 40 minutes).
Conclusion: They can only take the motorboat ride because the paddle boat exceeds their 40-minute time limit.
CBSE Step-by-Step Marking Scheme
Budget calculation for both boats (₹100 vs ₹60)
1.5 M
Time limit comparison selecting motorboat (20 mins vs 45 mins)
1.5 M
Q4
Fuel Arithmetic • Filling Bus Tanks
At a highway petrol pump, the driver filled 65 litres of diesel into a bus tank. If the diesel price was ₹84 per litre, calculate the total amount the school paid for the diesel.
[2 Marks]
✅ Step-by-Step Solution & Working
Multiplication Calculation:
6 5 litres
× 8 4 rupees
-----------
2 6 0 (65 × 4)
+ 5 2 0 0 (65 × 80)
-----------
5 4 6 0
The school paid ₹5,460 for the diesel.
6 5 litres
× 8 4 rupees
-----------
2 6 0 (65 × 4)
+ 5 2 0 0 (65 × 80)
-----------
5 4 6 0
The school paid ₹5,460 for the diesel.
CBSE Step-by-Step Marking Scheme
Correct partial products (260 and 5200)
1.0 M
Final total bill of ₹5,460
1.0 M
Q5
Building with Bricks • Brick Geometry & Measurement
A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long?
[3 Marks]
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long?
✅ Step-by-Step Solution & Working
Brick Mathematics:
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
CBSE Step-by-Step Marking Scheme
Cuboid shape
1 M
Area = 200 cm²
1 M
5 bricks
1 M
Q6
A Trip to Bhopal • Diesel Fuel Budget
During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay?
[3 Marks]
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay?
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
CBSE Step-by-Step Marking Scheme
200 litres
1.5 M
₹14,000 bill
1.5 M
Q7
Long and Short • Height Comparisons
The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)?
[2 Marks]
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)?
✅ Step-by-Step Solution & Working
Calculations:
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
CBSE Step-by-Step Marking Scheme
2 m 45 cm
1 M
5 cm difference
1 M
Q8
Tick-Tick-Tick • Expiry Dates on Food
A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.
[2 Marks]
✅ Step-by-Step Solution & Working
Date Verification:
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
CBSE Step-by-Step Marking Scheme
Time elapsed is ~90 days
1 M
Safe to consume within 180 days
1 M
Q9
The Junk Seller • Loan and Interest
Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank?
[3 Marks]
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank?
✅ Step-by-Step Solution & Working
Loan Repayment:
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
CBSE Step-by-Step Marking Scheme
Total repayment = ₹306
1.5 M
Interest = ₹6
1.5 M
Q10
Jugs and Mugs • Measuring Medicine Dose
A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last?
[3 Marks]
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last?
✅ Step-by-Step Solution & Working
Dosage Calculations:
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
CBSE Step-by-Step Marking Scheme
15 mL daily
1.5 M
Bottle lasts 10 days
1.5 M
Q11
Carts and Wheels • Circle Geometry
A cyclist has a bicycle wheel with a radius of 35 cm.
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle?
[2 Marks]
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle?
✅ Step-by-Step Solution & Working
Circle Properties:
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
CBSE Step-by-Step Marking Scheme
Diameter = 70 cm
1 M
Formula D = 2r stated
1 M
Q12
Halves and Quarters • Fraction Sharing
Raju has ₹100. He spends 1/2 of his money on a book, and 1/4 of his total money on a pen.
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left?
[3 Marks]
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left?
✅ Step-by-Step Solution & Working
Fractional Expenditure:
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
CBSE Step-by-Step Marking Scheme
Book = ₹50
1 M
Pen = ₹25
1 M
Remaining = ₹25
1 M
Q13
Play with Patterns • Secret Message Cipher
In a secret code, each letter is replaced by its position in the alphabet (A=1, B=2, C=3, ... Z=26).
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell?
[2 Marks]
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell?
✅ Step-by-Step Solution & Working
Decoding Cipher:
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
CBSE Step-by-Step Marking Scheme
Correct decoding to spell MATHS
2 M
Q14
Tables and Shares • Division with Remainder
A florist has 58 roses. She wants to make bouquets containing 6 roses each.
(a) How many complete bouquets can she make?
(b) How many roses will be left over?
[2 Marks]
(a) How many complete bouquets can she make?
(b) How many roses will be left over?
✅ Step-by-Step Solution & Working
Division:
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
CBSE Step-by-Step Marking Scheme
9 bouquets
1 M
4 leftover roses
1 M
Q15
Review Questions • True or False
State True or False:
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time.
[3 Marks]
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time.
✅ Step-by-Step Solution & Working
Answers:
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study
Petrol Pump Refueling Time
Two buses stop at a petrol pump to refill diesel. Each bus needs 50 litres of diesel. 1 litre of diesel costs ₹45. The pump fills diesel at a rate of 10 litres per minute.
Analytical Task: What is the total bill for both buses, and how long does it take to fill both buses?
Evaluation & Model Answer:
Step 1: Total diesel required:
2 buses × 50 litres = 100 litres.
Step 2: Total cost:
100 litres × ₹45/litre = ₹4,500.
Step 3: Total filling time:
100 litres ÷ 10 litres/min = 10 minutes.
2 buses × 50 litres = 100 litres.
Step 2: Total cost:
100 litres × ₹45/litre = ₹4,500.
Step 3: Total filling time:
100 litres ÷ 10 litres/min = 10 minutes.
Rubric: 1 Mark for cost ₹4,500; 1 Mark for time 10 minutes.