rohan2345 wrote:
Sam drove at a constant speed from City X along a highway to City Y. Did Sam reach City Y from City X in less than an hour?
(1) If Sam had driven at the same speed to City Z that was 15 kilometers further down the highway, he would have taken 50% more time
(2) If Sam's average speed for the drive had been 20 kilometers per hour lesser, he would have taken 50% more time
Solution: Pre Analysis:- Let the distance between X and Y be D and speed of Sam be S
- Then time to reach Y will be \(\frac{D}{S}\) and we are asked if \(\frac{D}{S}<1\) or not
Statement 1: If Sam had driven at the same speed to City Z that was 15 kilometers further down the highway, he would have taken 50% more time
- According to this statement, to move extra 15 km, it would have taken 50% more time i.e., \(\frac{50}{100}\times \frac{D}{S}=\frac{D}{2S}\)
- Or, we can say \(\frac{15}{S}=\frac{D}{2S}\) or \(D=30\)
- But we do not get the value of S or \(\frac{D}{S}\)
- Thus, statement 1 alone is not sufficient and we can eliminate options A and D
Statement 2: If Sam's average speed for the drive had been 20 kilometers per hour lesser, he would have taken 50% more time
- According to this statement, time when speed \(= S-20\) would have been 50% more than \(\frac{D}{S}\)
- Or we can say \(\frac{D}{S-20}=\frac{3D}{2S}\) or \(S=60\)
- But we do not get the value of D or \(\frac{D}{S}\)
Combining: - Upon combining we get the value of both D and S
Hence the right answer is
Option C