Given below are two statements based on the following: A car travels 25…
2022
Given below are two statements based on the following:
A car travels 25 km/hour faster than a bus for a journey of 500 km, and the bus takes 10 hours more than the car.
Statement I: Speed of the car is 45 km/hour.
Statement II: Speed of the bus is 20 km/hour.
Choose the correct answer from the options given below:
Answer: B. Both Statement I and Statement II are false — ConceptFor a fixed distance D, travel time is D/v. If the slower speed is x and the faster speed is x + d, a stated time difference Δt gives D/x − D/(x + d) =…
- A.
Both Statement I and Statement II are true
- B.
Both Statement I and Statement II are false
- C.
Statement I is true but Statement II is false
- D.
Statement I is false but Statement II is true
Attempted by 2 students.
Show answer & explanation
Correct answer: B
Concept
For a fixed distance D, travel time is D/v. If the slower speed is x and the faster speed is x + d, a stated time difference Δt gives D/x − D/(x + d) = Δt.
Only a positive speed is physically meaningful. After solving, substitute the speeds into both the speed-difference and time-difference conditions.
Application
Let the bus speed be x km/h; then the car speed is x + 25 km/h.
Using time = distance/speed, the bus time is 500/x hours and the car time is 500/(x + 25) hours.
The bus takes 10 hours more, so 500/x − 500/(x + 25) = 10.
Combining the fractions gives 12500/[x(x + 25)] = 10, hence x(x + 25) = 1250.
Therefore x2 + 25x − 1250 = 0 = (x − 25)(x + 50). The positive root is x = 25.
Thus the bus speed is 25 km/h and the car speed is 50 km/h. Statement I gives 45 km/h and Statement II gives 20 km/h, so neither statement matches the derived speeds.
Cross-check
Speed difference: 50 − 25 = 25 km/h.
Time difference: 500/25 − 500/50 = 20 − 10 = 10 hours.
Therefore, both Statement I and Statement II are false.