In a parking area, the total number of wheels of all the cars (four-wheelers) and scooters/motorbikes (two-wheelers) is 100 more than twice the number of parked vehicles. The number of cars parked is
- (a) 35
- (b) 45
- (c) 50 ✓ UPSC's answer
- (d) 55
Why the answer is (c)
• Let $C$ be the number of cars and $S$ be the number of scooters/motorbikes.
• The total number of vehicles is $C + S$.
• The total number of wheels is $4C + 2S$.
• The problem states that the total wheels are 100 more than twice the number of vehicles: $4C + 2S = 2(C + S) + 100$.
• Simplifying the equation: $4C + 2S = 2C + 2S + 100$.
• Subtracting $2S$ from both sides gives $4C = 2C + 100$, which simplifies to $2C = 100$, so $C = 50$.
Why the other options are wrong
- (a) 35
- Option (a) is incorrect because substituting 35 cars into the derived equation $2C = 100$ yields 70, not 100.
- (b) 45
- Option (b) is incorrect because substituting 45 cars into the derived equation $2C = 100$ yields 90, not 100.
- (d) 55
- Option (d) is incorrect because substituting 55 cars into the derived equation $2C = 100$ yields 110, not 100.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2015, held on 23 August 2015. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.