ZoomWheels, a self-drive car rental company, operates in four cities – Delhi, Mumbai, Bengaluru and Pune – and rents out four categories of cars: Hatchback, Sedan, SUV and Luxury. The daily rental charged for a car depends only on its category.
Table 1: Daily rental (₹ per car per day) and monthly maintenance cost (₹ per car per month)
| Category | Daily rental | Maintenance |
|---|---|---|
| Hatchback | 1,200 | 6,000 |
| Sedan | 2,000 | 9,000 |
| SUV | 3,000 | 15,000 |
| Luxury | 6,000 | 40,000 |
Table 2: Number of cars in the fleet in June
| City | Hatchback | Sedan | SUV | Luxury |
|---|---|---|---|---|
| Delhi | 40 | 25 | 20 | 5 |
| Mumbai | 35 | 30 | 15 | 8 |
| Bengaluru | 30 | 20 | 25 | 6 |
| Pune | 25 | 15 | 10 | 4 |
Table 3: Utilisation (%) in June
| City | Hatchback | Sedan | SUV | Luxury |
|---|---|---|---|---|
| Delhi | 80 | 80 | 75 | 60 |
| Mumbai | 90 | 90 | 80 | 75 |
| Bengaluru | 80 | 70 | 90 | 60 |
| Pune | 80 | 60 | 80 | 50 |
June has 30 days. Utilisation of a category in a city = (number of car-days rented) ÷ (number of cars × number of days in the month) × 100. Rental revenue = car-days rented × daily rental. Maintenance is incurred on every car in the fleet, whether rented or not. Operating profit = rental revenue − maintenance cost.
Table 1: Daily rental (₹ per car per day) and monthly maintenance cost (₹ per car per month)
| Category | Daily rental | Maintenance |
|---|---|---|
| Hatchback | 1,200 | 6,000 |
| Sedan | 2,000 | 9,000 |
| SUV | 3,000 | 15,000 |
| Luxury | 6,000 | 40,000 |
Table 2: Number of cars in the fleet in June
| City | Hatchback | Sedan | SUV | Luxury |
|---|---|---|---|---|
| Delhi | 40 | 25 | 20 | 5 |
| Mumbai | 35 | 30 | 15 | 8 |
| Bengaluru | 30 | 20 | 25 | 6 |
| Pune | 25 | 15 | 10 | 4 |
Table 3: Utilisation (%) in June
| City | Hatchback | Sedan | SUV | Luxury |
|---|---|---|---|---|
| Delhi | 80 | 80 | 75 | 60 |
| Mumbai | 90 | 90 | 80 | 75 |
| Bengaluru | 80 | 70 | 90 | 60 |
| Pune | 80 | 60 | 80 | 50 |
June has 30 days. Utilisation of a category in a city = (number of car-days rented) ÷ (number of cars × number of days in the month) × 100. Rental revenue = car-days rented × daily rental. Maintenance is incurred on every car in the fleet, whether rented or not. Operating profit = rental revenue − maintenance cost.
Question 1
Single correct option
Which city earned the highest rental revenue in June?
- A. Delhi
- B. Mumbai
- C. Bengaluru
- D. Pune
Show answer and solution
Answer: (B) Mumbai
Car-days rented = cars × 30 × utilisation. Revenue per city (₹ lakh):
| City | Hatch | Sedan | SUV | Luxury | Total |
|---|---|---|---|---|---|
| Delhi | 960 × 1200 = 11.52 | 600 × 2000 = 12.00 | 450 × 3000 = 13.50 | 90 × 6000 = 5.40 | 42.42 |
| Mumbai | 945 → 11.34 | 810 → 16.20 | 360 → 10.80 | 180 → 10.80 | 49.14 |
| Bengaluru | 720 → 8.64 | 420 → 8.40 | 675 → 20.25 | 108 → 6.48 | 43.77 |
| Pune | 600 → 7.20 | 270 → 5.40 | 240 → 7.20 | 60 → 3.60 | 23.40 |
Mumbai (₹49.14 lakh) is the highest. Bengaluru's big SUV revenue is not enough to overcome Mumbai's strong Sedan and Luxury figures.
Tip: Build the car-days table once – every question in this set uses it.
| City | Hatch | Sedan | SUV | Luxury | Total |
|---|---|---|---|---|---|
| Delhi | 960 × 1200 = 11.52 | 600 × 2000 = 12.00 | 450 × 3000 = 13.50 | 90 × 6000 = 5.40 | 42.42 |
| Mumbai | 945 → 11.34 | 810 → 16.20 | 360 → 10.80 | 180 → 10.80 | 49.14 |
| Bengaluru | 720 → 8.64 | 420 → 8.40 | 675 → 20.25 | 108 → 6.48 | 43.77 |
| Pune | 600 → 7.20 | 270 → 5.40 | 240 → 7.20 | 60 → 3.60 | 23.40 |
Mumbai (₹49.14 lakh) is the highest. Bengaluru's big SUV revenue is not enough to overcome Mumbai's strong Sedan and Luxury figures.
Tip: Build the car-days table once – every question in this set uses it.
Question 2
Numerical answer
What was the total rental revenue (in ₹ lakh) from SUVs across all four cities in June?
Show answer and solution
Answer: 51.75
SUV car-days = cars × 30 × utilisation:
- Delhi: 20 × 30 × 0.75 = 450
- Mumbai: 15 × 30 × 0.80 = 360
- Bengaluru: 25 × 30 × 0.90 = 675
- Pune: 10 × 30 × 0.80 = 240
Total = 1725 car-days. Revenue = 1725 × ₹3000 = ₹51,75,000 = ₹51.75 lakh.
Trap: Do not average the utilisation percentages (81.25%) and apply them to the total fleet – the cities have different fleet sizes, so a weighted calculation is needed.
- Delhi: 20 × 30 × 0.75 = 450
- Mumbai: 15 × 30 × 0.80 = 360
- Bengaluru: 25 × 30 × 0.90 = 675
- Pune: 10 × 30 × 0.80 = 240
Total = 1725 car-days. Revenue = 1725 × ₹3000 = ₹51,75,000 = ₹51.75 lakh.
Trap: Do not average the utilisation percentages (81.25%) and apply them to the total fleet – the cities have different fleet sizes, so a weighted calculation is needed.
Question 3
Single correct option
Considering all four cities together, which category of cars generated the highest operating profit in June?
- A. Hatchback
- B. Sedan
- C. SUV
- D. Luxury
Show answer and solution
Answer: (C) SUV
Revenue by category (all cities): Hatchback car-days = 960 + 945 + 720 + 600 = 3225 → ₹38.70 lakh; Sedan = 600 + 810 + 420 + 270 = 2100 → ₹42.00 lakh; SUV = 1725 → ₹51.75 lakh; Luxury = 90 + 180 + 108 + 60 = 438 → ₹26.28 lakh.
Maintenance (fleet × monthly cost): Hatchback 130 × 6000 = ₹7.80 lakh; Sedan 90 × 9000 = ₹8.10 lakh; SUV 70 × 15000 = ₹10.50 lakh; Luxury 23 × 40000 = ₹9.20 lakh.
Operating profit: Hatchback 30.90, Sedan 33.90, SUV 41.25, Luxury 17.08 (₹ lakh).
SUV is the highest. Luxury's high daily rental is offset by low utilisation and heavy maintenance.
Maintenance (fleet × monthly cost): Hatchback 130 × 6000 = ₹7.80 lakh; Sedan 90 × 9000 = ₹8.10 lakh; SUV 70 × 15000 = ₹10.50 lakh; Luxury 23 × 40000 = ₹9.20 lakh.
Operating profit: Hatchback 30.90, Sedan 33.90, SUV 41.25, Luxury 17.08 (₹ lakh).
SUV is the highest. Luxury's high daily rental is offset by low utilisation and heavy maintenance.
Question 4
Numerical answer
In July (31 days), Delhi added 10 Hatchbacks to its fleet, and the number of Hatchback car-days rented in Delhi rose by 20% over June. What was the utilisation (in %, rounded to the nearest integer) of Delhi's Hatchbacks in July?
Show answer and solution
Answer: 74
June Hatchback car-days in Delhi = 40 × 30 × 0.80 = 960.
July car-days = 960 × 1.2 = 1152.
July capacity = (40 + 10) cars × 31 days = 1550 car-days.
Utilisation = 1152 ÷ 1550 × 100 = 74.32% ≈ 74%.
Trap: Using 30 days for July gives 1152/1500 = 76.8%, and forgetting the extra cars gives 1152/1240 = 92.9%. Note that utilisation fell even though demand rose, because capacity rose faster (25% more cars and one extra day).
July car-days = 960 × 1.2 = 1152.
July capacity = (40 + 10) cars × 31 days = 1550 car-days.
Utilisation = 1152 ÷ 1550 × 100 = 74.32% ≈ 74%.
Trap: Using 30 days for July gives 1152/1500 = 76.8%, and forgetting the extra cars gives 1152/1240 = 92.9%. Note that utilisation fell even though demand rose, because capacity rose faster (25% more cars and one extra day).
Question 5
Single correct option
In June, what is the minimum number of additional Luxury car-days that Pune would have needed to rent so that its Luxury rental revenue was at least equal to its Sedan rental revenue?
- A. 30
- B. 20
- C. 45
- D. 60
Show answer and solution
Answer: (A) 30
Pune Sedan revenue = 15 × 30 × 0.60 = 270 car-days × ₹2000 = ₹5,40,000.
Pune Luxury car-days = 4 × 30 × 0.50 = 60, revenue = 60 × ₹6000 = ₹3,60,000.
To reach ₹5,40,000, Luxury needs 540000 ÷ 6000 = 90 car-days, i.e. 90 − 60 = 30 more car-days.
Feasibility check: 90 ≤ 4 × 30 = 120 available Luxury car-days, so this is achievable (utilisation 75%).
Why others fail: 45 comes from dividing the ₹1.8 lakh gap by the Hatchback-style rate of ₹4000; 60 doubles the current car-days; 20 ignores the rate difference.
Pune Luxury car-days = 4 × 30 × 0.50 = 60, revenue = 60 × ₹6000 = ₹3,60,000.
To reach ₹5,40,000, Luxury needs 540000 ÷ 6000 = 90 car-days, i.e. 90 − 60 = 30 more car-days.
Feasibility check: 90 ≤ 4 × 30 = 120 available Luxury car-days, so this is achievable (utilisation 75%).
Why others fail: 45 comes from dividing the ₹1.8 lakh gap by the Hatchback-style rate of ₹4000; 60 doubles the current car-days; 20 ignores the rate difference.
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