Chapter 4 of 15
Chapter 4: We the Travellers – II
हम यात्री – २ (यात्रा व्यय, होटल पैकेज एवं दैनिक बजट) | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- Multi-digit addition and subtraction applied to travel logistics and ticket reservations.
- Comparing hotel packages: Flat rate vs Room-plus-meal split pricing.
- Taxi fare calculations with minimum distance billing criteria.
- Fuel economy, distance per litre, and total trip expenditure.
All Textbook Exercises & In-Text Tasks (24 Questions)
100% Complete Ingestion
Q1
Travel Budget • Hotel Package Comparison
A hotel offers two package options for a 3-night stay for a family of 4:
• Package A: Flat rate of ₹2,800 per night including breakfast.
• Package B: Room rent of ₹2,200 per night plus ₹250 per person per day for breakfast.
(a) Calculate the total cost for Package A.
(b) Calculate the total cost for Package B.
(c) Which package is more economical, and by how much?
[3 Marks]
• Package A: Flat rate of ₹2,800 per night including breakfast.
• Package B: Room rent of ₹2,200 per night plus ₹250 per person per day for breakfast.
(a) Calculate the total cost for Package A.
(b) Calculate the total cost for Package B.
(c) Which package is more economical, and by how much?
✅ Step-by-Step Solution & Working
Calculations (Duration = 3 nights, 4 persons):
• (a) Package A Total: 3 nights × ₹2,800 = ₹8,400.
• (b) Package B Total:
- Room rent: 3 × ₹2,200 = ₹6,600.
- Breakfast cost: 4 persons × ₹250 × 3 days = ₹3,000.
- Total = ₹6,600 + ₹3,000 = ₹9,600.
• (c) Comparison: Package A is cheaper. Difference = ₹9,600 - ₹8,400 = ₹1,200. Package A saves ₹1,200.
• (a) Package A Total: 3 nights × ₹2,800 = ₹8,400.
• (b) Package B Total:
- Room rent: 3 × ₹2,200 = ₹6,600.
- Breakfast cost: 4 persons × ₹250 × 3 days = ₹3,000.
- Total = ₹6,600 + ₹3,000 = ₹9,600.
• (c) Comparison: Package A is cheaper. Difference = ₹9,600 - ₹8,400 = ₹1,200. Package A saves ₹1,200.
CBSE Step-by-Step Marking Scheme
Package A = ₹8,400
1.0 M
Package B = ₹9,600
1.0 M
Package A saves ₹1,200
1.0 M
Q2
Excursion Expenses • Per-Student Share
A school excursion of 45 students incurs expenses:
• Bus rental: ₹14,500
• Entry tickets: ₹90 per student
• Packed meals: ₹150 per student
• Guide charges: ₹1,500
(a) Find the grand total expenditure for the trip.
(b) Calculate the contribution amount required from each student to cover all costs exactly.
[3 Marks]
• Bus rental: ₹14,500
• Entry tickets: ₹90 per student
• Packed meals: ₹150 per student
• Guide charges: ₹1,500
(a) Find the grand total expenditure for the trip.
(b) Calculate the contribution amount required from each student to cover all costs exactly.
✅ Step-by-Step Solution & Working
Expense Calculations (45 Students):
• Bus rental = ₹14,500
• Entry tickets = 45 × ₹90 = ₹4,050
• Packed meals = 45 × ₹150 = ₹6,750
• Guide charges = ₹1,500
• (a) Grand Total: ₹14,500 + ₹4,050 + ₹6,750 + ₹1,500 = ₹26,800.
• (b) Per Student Share: ₹26,800 ÷ 45 = ₹595.55 ≈ ₹596 per student.
• Bus rental = ₹14,500
• Entry tickets = 45 × ₹90 = ₹4,050
• Packed meals = 45 × ₹150 = ₹6,750
• Guide charges = ₹1,500
• (a) Grand Total: ₹14,500 + ₹4,050 + ₹6,750 + ₹1,500 = ₹26,800.
• (b) Per Student Share: ₹26,800 ÷ 45 = ₹595.55 ≈ ₹596 per student.
CBSE Step-by-Step Marking Scheme
Itemized totals (Tickets ₹4,050, Meals ₹6,750)
1.0 M
Grand total = ₹26,800
1.0 M
Per student share = ₹596
1.0 M
Q3
Fuel Consumption & Cost
A family car consumes 1 litre of petrol for every 15 km traveled. They plan a road trip of 1,080 km.
(a) How many litres of petrol are required for the round trip?
(b) If petrol costs ₹96 per litre, what is their total expenditure on fuel?
[3 Marks]
(a) How many litres of petrol are required for the round trip?
(b) If petrol costs ₹96 per litre, what is their total expenditure on fuel?
✅ Step-by-Step Solution & Working
Calculations:
• (a) Petrol Needed: Total distance ÷ Mileage = 1,080 ÷ 15 = 72 litres.
• (b) Fuel Cost: 72 litres × ₹96 = ₹6,912.
• (a) Petrol Needed: Total distance ÷ Mileage = 1,080 ÷ 15 = 72 litres.
• (b) Fuel Cost: 72 litres × ₹96 = ₹6,912.
CBSE Step-by-Step Marking Scheme
Petrol needed = 72 L
1.5 M
Total fuel cost = ₹6,912
1.5 M
Q4
Bus vs Train Travel Cost
A tour group of 28 persons travels from Delhi to Agra (240 km).
• Option 1: AC Bus charter costs a flat ₹11,200.
• Option 2: Train tickets cost ₹385 per person.
(a) Calculate the cost for all 28 people traveling by train.
(b) Which option is more cost-effective and by how much?
[3 Marks]
• Option 1: AC Bus charter costs a flat ₹11,200.
• Option 2: Train tickets cost ₹385 per person.
(a) Calculate the cost for all 28 people traveling by train.
(b) Which option is more cost-effective and by how much?
✅ Step-by-Step Solution & Working
Working:
• (a) Train Cost: 28 × ₹385 = ₹10,780.
• (b) Comparison:
- Bus = ₹11,200
- Train = ₹10,780
- Difference = ₹11,200 - ₹10,780 = ₹420.
Traveling by train is more economical by ₹420.
• (a) Train Cost: 28 × ₹385 = ₹10,780.
• (b) Comparison:
- Bus = ₹11,200
- Train = ₹10,780
- Difference = ₹11,200 - ₹10,780 = ₹420.
Traveling by train is more economical by ₹420.
CBSE Step-by-Step Marking Scheme
Train cost = ₹10,780
1.5 M
Train is cheaper by ₹420
1.5 M
Q5
Unitary Method • Meal Charges
A highway restaurant charges ₹480 for 4 thalis.
(a) What is the cost of 1 thali?
(b) What will be the total bill for 9 thalis?
(c) How many thalis can be purchased for ₹1,200?
[3 Marks]
(a) What is the cost of 1 thali?
(b) What will be the total bill for 9 thalis?
(c) How many thalis can be purchased for ₹1,200?
✅ Step-by-Step Solution & Working
Unitary Method Steps:
• (a) Cost of 1 Thali: ₹480 ÷ 4 = ₹120.
• (b) Cost of 9 Thalis: 9 × ₹120 = ₹1,080.
• (c) Thalis for ₹1,200: ₹1,200 ÷ ₹120 = 10 thalis.
• (a) Cost of 1 Thali: ₹480 ÷ 4 = ₹120.
• (b) Cost of 9 Thalis: 9 × ₹120 = ₹1,080.
• (c) Thalis for ₹1,200: ₹1,200 ÷ ₹120 = 10 thalis.
CBSE Step-by-Step Marking Scheme
Cost of 1 thali = ₹120
1.0 M
Cost of 9 thalis = ₹1,080
1.0 M
10 thalis for ₹1,200
1.0 M
Q6
Time-Speed-Distance • Multi-Stop Journey
A luxury bus leaves Jaipur at 6:00 AM. It travels at 60 km/h for 3 hours, stops for 45 minutes for breakfast, and then travels the remaining 140 km at 70 km/h.
(a) What is the total distance of the trip?
(b) What was the travel time spent driving?
(c) At what time does the bus reach its destination?
[3 Marks]
(a) What is the total distance of the trip?
(b) What was the travel time spent driving?
(c) At what time does the bus reach its destination?
✅ Step-by-Step Solution & Working
Step-by-Step Schedule:
• (a) Distance: First leg = 3 h × 60 km/h = 180 km. Second leg = 140 km. Total distance = 180 + 140 = 320 km.
• (b) Driving Time: First leg = 3 hours. Second leg = 140 ÷ 70 = 2 hours. Total driving time = 3 + 2 = 5 hours.
• (c) Arrival Time:
- Total elapsed time = 5 hours driving + 45 min breakfast = 5 hours 45 minutes.
- 6:00 AM + 5 h 45 min = 11:45 AM.
• (a) Distance: First leg = 3 h × 60 km/h = 180 km. Second leg = 140 km. Total distance = 180 + 140 = 320 km.
• (b) Driving Time: First leg = 3 hours. Second leg = 140 ÷ 70 = 2 hours. Total driving time = 3 + 2 = 5 hours.
• (c) Arrival Time:
- Total elapsed time = 5 hours driving + 45 min breakfast = 5 hours 45 minutes.
- 6:00 AM + 5 h 45 min = 11:45 AM.
CBSE Step-by-Step Marking Scheme
Total distance = 320 km
1.0 M
Driving time = 5 hours
1.0 M
Arrival time = 11:45 AM
1.0 M
Q7
Group Travel Billing • GST Calculation
A travel agency bills ₹35,000 for a houseboat package in Kashmir. A government Goods and Services Tax (GST) of 5% is added to the bill.
(a) Find the GST amount in Rupees.
(b) What is the final total payable amount?
[3 Marks]
(a) Find the GST amount in Rupees.
(b) What is the final total payable amount?
✅ Step-by-Step Solution & Working
Percentage Calculation:
• (a) GST Amount: 5% of ₹35,000 = (5 ÷ 100) × 35,000 = 5 × 350 = ₹1,750.
• (b) Final Total: ₹35,000 + ₹1,750 = ₹36,750.
• (a) GST Amount: 5% of ₹35,000 = (5 ÷ 100) × 35,000 = 5 × 350 = ₹1,750.
• (b) Final Total: ₹35,000 + ₹1,750 = ₹36,750.
CBSE Step-by-Step Marking Scheme
GST = ₹1,750
1.5 M
Final bill = ₹36,750
1.5 M
Q8
Souvenir Shopping • Currency Exchange
A foreign tourist changes 150 US Dollars at an exchange counter. The exchange rate is 1 USD = ₹82.
(a) How many Indian Rupees does the tourist receive?
(b) He buys 3 wooden handicrafts costing ₹2,400 each and 2 silk shawls costing ₹1,800 each. How much money does he spend?
(c) How many Indian Rupees does he have left?
[3 Marks]
(a) How many Indian Rupees does the tourist receive?
(b) He buys 3 wooden handicrafts costing ₹2,400 each and 2 silk shawls costing ₹1,800 each. How much money does he spend?
(c) How many Indian Rupees does he have left?
✅ Step-by-Step Solution & Working
Calculations:
• (a) Rupees Received: 150 × ₹82 = ₹12,300.
• (b) Total Spent:
- 3 handicrafts: 3 × ₹2,400 = ₹7,200.
- 2 shawls: 2 × ₹1,800 = ₹3,600.
- Total spent = ₹7,200 + ₹3,600 = ₹10,800.
• (c) Balance: ₹12,300 - ₹10,800 = ₹1,500.
• (a) Rupees Received: 150 × ₹82 = ₹12,300.
• (b) Total Spent:
- 3 handicrafts: 3 × ₹2,400 = ₹7,200.
- 2 shawls: 2 × ₹1,800 = ₹3,600.
- Total spent = ₹7,200 + ₹3,600 = ₹10,800.
• (c) Balance: ₹12,300 - ₹10,800 = ₹1,500.
CBSE Step-by-Step Marking Scheme
Converted rupees = ₹12,300
1.0 M
Total expenditure = ₹10,800
1.0 M
Balance = ₹1,500
1.0 M
Q9
Luggage Allowance • Excess Baggage
An airline allows each passenger 15 kg of free check-in luggage. Extra baggage is charged at ₹350 per kg.
(a) Mr. Verma's suitcase weighs 22 kg. How many kg is he overweight?
(b) How much extra baggage fee must he pay?
[3 Marks]
(a) Mr. Verma's suitcase weighs 22 kg. How many kg is he overweight?
(b) How much extra baggage fee must he pay?
✅ Step-by-Step Solution & Working
Calculations:
• (a) Excess Weight: 22 kg - 15 kg = 7 kg excess.
• (b) Excess Fee: 7 kg × ₹350 = ₹2,450.
• (a) Excess Weight: 22 kg - 15 kg = 7 kg excess.
• (b) Excess Fee: 7 kg × ₹350 = ₹2,450.
CBSE Step-by-Step Marking Scheme
Excess weight = 7 kg
1.5 M
Extra fee = ₹2,450
1.5 M
Q10
Multiplication by Multiples of 10
Calculate quickly using mental math rules:
(a) 45 × 200
(b) 60 × 700
(c) 1,500 × 40
[3 Marks]
(a) 45 × 200
(b) 60 × 700
(c) 1,500 × 40
✅ Step-by-Step Solution & Working
Mental Calculations:
• (a) 45 × 200: 45 × 2 = 90, append two zeros → 9,000.
• (b) 60 × 700: 6 × 7 = 42, append three zeros → 42,000.
• (c) 1,500 × 40: 15 × 4 = 60, append three zeros → 60,000.
• (a) 45 × 200: 45 × 2 = 90, append two zeros → 9,000.
• (b) 60 × 700: 6 × 7 = 42, append three zeros → 42,000.
• (c) 1,500 × 40: 15 × 4 = 60, append three zeros → 60,000.
CBSE Step-by-Step Marking Scheme
Part (a): 9,000
1.0 M
Part (b): 42,000
1.0 M
Part (c): 60,000
1.0 M
Q11
Ropeway Cable Car Fare • Adult & Child
A mountain ropeway charges ₹220 for an adult round trip and ₹140 for a child under 12 years.
(a) What is the total ropeway cost for a family of 3 adults and 2 children?
(b) If they pay with a ₹2,000 note, how much change is returned?
[3 Marks]
(a) What is the total ropeway cost for a family of 3 adults and 2 children?
(b) If they pay with a ₹2,000 note, how much change is returned?
✅ Step-by-Step Solution & Working
Working:
• (a) Total Cost:
- Adults: 3 × ₹220 = ₹660.
- Children: 2 × ₹140 = ₹280.
- Total = ₹660 + ₹280 = ₹940.
• (b) Change: ₹2,000 - ₹940 = ₹1,060.
• (a) Total Cost:
- Adults: 3 × ₹220 = ₹660.
- Children: 2 × ₹140 = ₹280.
- Total = ₹660 + ₹280 = ₹940.
• (b) Change: ₹2,000 - ₹940 = ₹1,060.
CBSE Step-by-Step Marking Scheme
Adults ₹660, Children ₹280
1.0 M
Total ₹940
1.0 M
Change ₹1,060
1.0 M
Q12
Estimation of Travel Expenses
Estimate the total cost by rounding each item to the nearest hundred:
• Petrol: ₹3,240
• Food: ₹1,890
• Toll tax: ₹460
• Sightseeing tickets: ₹1,120
[3 Marks]
• Petrol: ₹3,240
• Food: ₹1,890
• Toll tax: ₹460
• Sightseeing tickets: ₹1,120
✅ Step-by-Step Solution & Working
Rounding to Nearest 100:
• Petrol: ₹3,240 rounds to ₹3,200.
• Food: ₹1,890 rounds to ₹1,900.
• Toll tax: ₹460 rounds to ₹500.
• Sightseeing tickets: ₹1,120 rounds to ₹1,100.
• Estimated Total: ₹3,200 + ₹1,900 + ₹500 + ₹1,100 = ₹6,700.
(Exact sum = ₹6,710; difference is only ₹10).
• Petrol: ₹3,240 rounds to ₹3,200.
• Food: ₹1,890 rounds to ₹1,900.
• Toll tax: ₹460 rounds to ₹500.
• Sightseeing tickets: ₹1,120 rounds to ₹1,100.
• Estimated Total: ₹3,200 + ₹1,900 + ₹500 + ₹1,100 = ₹6,700.
(Exact sum = ₹6,710; difference is only ₹10).
CBSE Step-by-Step Marking Scheme
Correct individual rounding
1.5 M
Estimated sum = ₹6,700
1.5 M
Q13
Speed & Time Variation • Traffic Delay
Normally, a taxi takes 2 hours to travel 120 km from the airport to the city centre. Due to heavy rain and traffic, the speed drops to 40 km/h.
(a) What was the normal speed of the taxi?
(b) How long does the journey take in the rain?
(c) How much extra time was lost in traffic?
[3 Marks]
(a) What was the normal speed of the taxi?
(b) How long does the journey take in the rain?
(c) How much extra time was lost in traffic?
✅ Step-by-Step Solution & Working
Calculations:
• (a) Normal Speed: 120 km ÷ 2 h = 60 km/h.
• (b) Rainy Journey Time: 120 km ÷ 40 km/h = 3 hours.
• (c) Extra Time Lost: 3 hours - 2 hours = 1 hour (60 minutes).
• (a) Normal Speed: 120 km ÷ 2 h = 60 km/h.
• (b) Rainy Journey Time: 120 km ÷ 40 km/h = 3 hours.
• (c) Extra Time Lost: 3 hours - 2 hours = 1 hour (60 minutes).
CBSE Step-by-Step Marking Scheme
Normal speed = 60 km/h
1.0 M
Rainy time = 3 hours
1.0 M
Time lost = 1 hour
1.0 M
Q14
Multi-Family Travel Split
Three families rent a vacation villa for 4 days at ₹6,500 per day. They share the accommodation cost equally.
(a) Find the total rent of the villa for 4 days.
(b) What is the share of each family?
(c) If Family 1 checks out one day early (staying 3 days), how should the total bill be divided fairly among the 3 families based on room-days?
[3 Marks]
(a) Find the total rent of the villa for 4 days.
(b) What is the share of each family?
(c) If Family 1 checks out one day early (staying 3 days), how should the total bill be divided fairly among the 3 families based on room-days?
✅ Step-by-Step Solution & Working
Working:
• (a) Total Rent: 4 days × ₹6,500 = ₹26,000.
• (b) Equal Share (All 4 days): ₹26,000 ÷ 3 = ₹8,666.67 per family.
• (c) Fair Room-Days Division:
- Total family-days = 3 + 4 + 4 = 11 family-days.
- Cost per family-day = ₹26,000 ÷ 11 = ₹2,363.64.
- Family 1 (3 days) pays: 3 × ₹2,363.64 = ₹7,091.
- Family 2 & 3 (4 days each) pay: 4 × ₹2,363.64 = ₹9,454.50 each.
• (a) Total Rent: 4 days × ₹6,500 = ₹26,000.
• (b) Equal Share (All 4 days): ₹26,000 ÷ 3 = ₹8,666.67 per family.
• (c) Fair Room-Days Division:
- Total family-days = 3 + 4 + 4 = 11 family-days.
- Cost per family-day = ₹26,000 ÷ 11 = ₹2,363.64.
- Family 1 (3 days) pays: 3 × ₹2,363.64 = ₹7,091.
- Family 2 & 3 (4 days each) pay: 4 × ₹2,363.64 = ₹9,454.50 each.
CBSE Step-by-Step Marking Scheme
Total rent = ₹26,000
1.0 M
Equal share = ₹8,667
1.0 M
Weighted room-days split
1.0 M
Q15
Train Berth Allotment • Logic
In an Indian Railways sleeper coach, berths are numbered 1 to 72. Lower berths are 1, 4, 9, 12, 17, 20... (numbers leaving remainders 1 or 4 when divided by 8).
(a) What type of berth is Berth 25?
(b) What type of berth is Berth 32?
[3 Marks]
(a) What type of berth is Berth 25?
(b) What type of berth is Berth 32?
✅ Step-by-Step Solution & Working
Berth Pattern in 8-berth Compartment:
• 1: Lower, 2: Middle, 3: Upper, 4: Lower, 5: Middle, 6: Upper, 7: Side Lower, 8: Side Upper.
• (a) Berth 25: 25 ÷ 8 gives remainder 1. Remainder 1 corresponds to a Lower Berth.
• (b) Berth 32: 32 ÷ 8 gives remainder 0 (exact multiple of 8). This corresponds to a Side Upper Berth (SU).
• 1: Lower, 2: Middle, 3: Upper, 4: Lower, 5: Middle, 6: Upper, 7: Side Lower, 8: Side Upper.
• (a) Berth 25: 25 ÷ 8 gives remainder 1. Remainder 1 corresponds to a Lower Berth.
• (b) Berth 32: 32 ÷ 8 gives remainder 0 (exact multiple of 8). This corresponds to a Side Upper Berth (SU).
CBSE Step-by-Step Marking Scheme
Berth pattern rule stated (modulo 8)
1.5 M
Berth 25 is Lower; Berth 32 is Side Upper
1.5 M
Q16
Fuel Tank Capacity • Kilometer Range
An SUV has a 65-litre fuel tank. Its highway mileage is 14 km/litre.
(a) What is the maximum driving range of the vehicle on a full tank?
(b) The driver sees a warning that 12 litres of petrol remain. Can the SUV reach a petrol station 180 km away without refueling?
[3 Marks]
(a) What is the maximum driving range of the vehicle on a full tank?
(b) The driver sees a warning that 12 litres of petrol remain. Can the SUV reach a petrol station 180 km away without refueling?
✅ Step-by-Step Solution & Working
Working:
• (a) Maximum Range: 65 L × 14 km/L = 910 km.
• (b) Remaining Range: 12 L × 14 km/L = 168 km.
- Since 168 km < 180 km, No, the SUV cannot reach the station 180 km away without refueling (it will run out of fuel 12 km before reaching).
• (a) Maximum Range: 65 L × 14 km/L = 910 km.
• (b) Remaining Range: 12 L × 14 km/L = 168 km.
- Since 168 km < 180 km, No, the SUV cannot reach the station 180 km away without refueling (it will run out of fuel 12 km before reaching).
CBSE Step-by-Step Marking Scheme
Max range = 910 km
1.5 M
Remaining range = 168 km with negative conclusion
1.5 M
Q17
Group Dining Bill • Split Evenly
Six friends dine at a restaurant during their trip. The food bill is ₹2,850 and service charge is ₹150.
(a) What is the total bill?
(b) If they split the cost equally among the 6 friends, how much does each person contribute?
[3 Marks]
(a) What is the total bill?
(b) If they split the cost equally among the 6 friends, how much does each person contribute?
✅ Step-by-Step Solution & Working
Working:
• (a) Total Bill: ₹2,850 + ₹150 = ₹3,000.
• (b) Individual Share: ₹3,000 ÷ 6 = ₹500 per person.
• (a) Total Bill: ₹2,850 + ₹150 = ₹3,000.
• (b) Individual Share: ₹3,000 ÷ 6 = ₹500 per person.
CBSE Step-by-Step Marking Scheme
Total bill = ₹3,000
1.5 M
Per person = ₹500
1.5 M
Q18
Sightseeing Boat Hire • Hourly Rate
A pedal boat costs ₹180 for 30 minutes, while a motor boat costs ₹450 for 20 minutes.
(a) Find the cost per minute for the pedal boat.
(b) Find the cost per minute for the motor boat.
(c) Which boat has a higher per-minute rate and by how much?
[3 Marks]
(a) Find the cost per minute for the pedal boat.
(b) Find the cost per minute for the motor boat.
(c) Which boat has a higher per-minute rate and by how much?
✅ Step-by-Step Solution & Working
Rate Calculations:
• (a) Pedal Boat Rate: ₹180 ÷ 30 min = ₹6 per minute.
• (b) Motor Boat Rate: ₹450 ÷ 20 min = ₹22.50 per minute.
• (c) Difference: ₹22.50 - ₹6.00 = ₹16.50 per minute higher for the motor boat.
• (a) Pedal Boat Rate: ₹180 ÷ 30 min = ₹6 per minute.
• (b) Motor Boat Rate: ₹450 ÷ 20 min = ₹22.50 per minute.
• (c) Difference: ₹22.50 - ₹6.00 = ₹16.50 per minute higher for the motor boat.
CBSE Step-by-Step Marking Scheme
Pedal boat = ₹6/min
1.0 M
Motor boat = ₹22.50/min
1.0 M
Difference = ₹16.50/min
1.0 M
Q19
HOTS • Travel Riddle
A train leaves City A and City B at the same time, traveling toward each other along parallel tracks. Train 1 travels at 60 km/h and Train 2 travels at 80 km/h. If the cities are 420 km apart, after how many hours will the trains meet?
[3 Marks]
✅ Step-by-Step Solution & Working
Relative Speed Concept:
1. Since the trains are moving toward each other, their combined speed is: 60 km/h + 80 km/h = 140 km/h.
2. Total distance to cover = 420 km.
3. Time taken to meet = Distance ÷ Relative Speed = 420 ÷ 140 = 3 hours.
4. Verification: In 3 hours, Train 1 covers 3 × 60 = 180 km; Train 2 covers 3 × 80 = 240 km. Total = 180 + 240 = 420 km. Verified!
1. Since the trains are moving toward each other, their combined speed is: 60 km/h + 80 km/h = 140 km/h.
2. Total distance to cover = 420 km.
3. Time taken to meet = Distance ÷ Relative Speed = 420 ÷ 140 = 3 hours.
4. Verification: In 3 hours, Train 1 covers 3 × 60 = 180 km; Train 2 covers 3 × 80 = 240 km. Total = 180 + 240 = 420 km. Verified!
CBSE Step-by-Step Marking Scheme
Combined speed = 140 km/h
1.5 M
Meeting time = 3 hours with verification
1.5 M
Q20
Airfare Surge Pricing • Mental Math
A base air ticket is ₹3,500. During festival season, the airline applies a surge increase of 40%.
(a) What is the surge price increase in Rupees?
(b) What is the new ticket price?
[3 Marks]
(a) What is the surge price increase in Rupees?
(b) What is the new ticket price?
✅ Step-by-Step Solution & Working
Calculations:
• (a) Surge Amount: 40% of ₹3,500 = (40 ÷ 100) × 3,500 = 40 × 35 = ₹1,400.
• (b) New Price: ₹3,500 + ₹1,400 = ₹4,900.
• (a) Surge Amount: 40% of ₹3,500 = (40 ÷ 100) × 3,500 = 40 × 35 = ₹1,400.
• (b) New Price: ₹3,500 + ₹1,400 = ₹4,900.
CBSE Step-by-Step Marking Scheme
Surge increase = ₹1,400
1.5 M
New price = ₹4,900
1.5 M
Q21
Bus Ticket Booking Agent Commission
A booking agent earns a commission of ₹45 on every bus ticket booked. In one week, he books 160 tickets.
(a) Find his total earnings for the week.
(b) If his weekly target was ₹8,000, by how much did he fall short or exceed his target?
[3 Marks]
(a) Find his total earnings for the week.
(b) If his weekly target was ₹8,000, by how much did he fall short or exceed his target?
✅ Step-by-Step Solution & Working
Calculations:
• (a) Total Earnings: 160 × ₹45 = ₹7,200.
• (b) Target Difference: ₹8,000 - ₹7,200 = ₹800 short of target.
• (a) Total Earnings: 160 × ₹45 = ₹7,200.
• (b) Target Difference: ₹8,000 - ₹7,200 = ₹800 short of target.
CBSE Step-by-Step Marking Scheme
Earnings = ₹7,200
1.5 M
Short by ₹800
1.5 M
Q22
Multi-Day Mileage Log Analysis
A touring taxi records its daily kilometres:
Day 1: 345 km, Day 2: 412 km, Day 3: 288 km, Day 4: 355 km.
(a) Find the total distance traveled over the 4 days.
(b) Find the average daily distance traveled.
[3 Marks]
Day 1: 345 km, Day 2: 412 km, Day 3: 288 km, Day 4: 355 km.
(a) Find the total distance traveled over the 4 days.
(b) Find the average daily distance traveled.
✅ Step-by-Step Solution & Working
Calculations:
• (a) Total Distance: 345 + 412 + 288 + 355 = 1,400 km.
• (b) Average Daily Distance: Total distance ÷ 4 days = 1,400 ÷ 4 = 350 km per day.
• (a) Total Distance: 345 + 412 + 288 + 355 = 1,400 km.
• (b) Average Daily Distance: Total distance ÷ 4 days = 1,400 ÷ 4 = 350 km per day.
CBSE Step-by-Step Marking Scheme
Total = 1,400 km
1.5 M
Average = 350 km/day
1.5 M
Q23
Currency Denominations • Cash Settlement
To settle a hotel bill of ₹7,850, a traveler gives four ₹2,000 notes.
(a) What is the total cash tendered?
(b) How much change should the cashier return?
(c) What is the minimum number of currency notes (using ₹500, ₹100, and ₹50 notes) that can make up this change?
[3 Marks]
(a) What is the total cash tendered?
(b) How much change should the cashier return?
(c) What is the minimum number of currency notes (using ₹500, ₹100, and ₹50 notes) that can make up this change?
✅ Step-by-Step Solution & Working
Cash Calculations:
• (a) Cash Tendered: 4 × ₹2,000 = ₹8,000.
• (b) Change: ₹8,000 - ₹7,850 = ₹150.
• (c) Minimum Notes for ₹150: One ₹100 note + One ₹50 note = 2 notes.
• (a) Cash Tendered: 4 × ₹2,000 = ₹8,000.
• (b) Change: ₹8,000 - ₹7,850 = ₹150.
• (c) Minimum Notes for ₹150: One ₹100 note + One ₹50 note = 2 notes.
CBSE Step-by-Step Marking Scheme
Cash tendered = ₹8,000
1.0 M
Change = ₹150
1.0 M
Minimum notes = 2 (₹100 + ₹50)
1.0 M
Q24
Comprehensive Travel Review
A family sets aside a vacation budget of ₹50,000. Their actual expenses are: Travel ₹18,600, Hotel ₹16,400, Food ₹8,500, Shopping ₹4,750.
(a) What is the total money spent?
(b) Did they stay within their budget? How much money remains or by how much did they exceed?
[3 Marks]
(a) What is the total money spent?
(b) Did they stay within their budget? How much money remains or by how much did they exceed?
✅ Step-by-Step Solution & Working
Financial Review:
• (a) Total Expenses: ₹18,600 + ₹16,400 + ₹8,500 + ₹4,750 = ₹48,250.
• (b) Budget Comparison: Budget = ₹50,000. Difference = ₹50,000 - ₹48,250 = ₹1,750.
Yes, they stayed within budget, saving ₹1,750.
• (a) Total Expenses: ₹18,600 + ₹16,400 + ₹8,500 + ₹4,750 = ₹48,250.
• (b) Budget Comparison: Budget = ₹50,000. Difference = ₹50,000 - ₹48,250 = ₹1,750.
Yes, they stayed within budget, saving ₹1,750.
CBSE Step-by-Step Marking Scheme
Total expenses = ₹48,250
1.5 M
Stayed within budget with ₹1,750 left
1.5 M
🌟 NEP 2020 Competency-Based Case Study
Competency Question: Taxi Billing with Minimum Distance Threshold
A taxi operator charges a flat hire of ₹2,500 per day covering up to 250 km. Any extra distance above 250 km in a day is billed at ₹12 per km. On a 3-day tour, the odometer readings showed: Day 1: 240 km; Day 2: 290 km; Day 3: 275 km.
Analytical Task: Calculate the total billing for each of the 3 days and the overall bill for the trip.
Evaluation & Model Answer:
Suggested Model Solution:
Day 1 (240 km): < 250 km ⇒ Flat rate = ₹2,500.
Day 2 (290 km): Extra = 40 km ⇒ ₹2,500 + (40 × 12) = ₹2,980.
Day 3 (275 km): Extra = 25 km ⇒ ₹2,500 + (25 × 12) = ₹2,800.
Grand Total: 2,500 + 2,980 + 2,800 = ₹8,280.
Rubric: 1M concept identification + 1M step execution + 1M conclusion