Question : A covered a distance of 240 km at a certain speed. Had his speed been 8 km/hr less, then the time taken would have been one hour more for covering the same distance. How much time (in hours) will he take to cover a distance of 480 km at his original speed?
Option 1: 9
Option 2: 11
Option 3: 10
Option 4: 8
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Correct Answer: 10
Solution : Let the original speed be S and the original time T. Then, according to the question ⇒ (S – 8) × (T + 1) = 240 [Speed × Time = Distance] Also, T = $\frac{240}{S}$ Now, (S – 8)×($\frac{240}{S}$ + 1) = 240 ⇒ 240S = (S – 8) × (240 + S) ⇒ 240S = 240S + S 2 − 8S − 1920 ⇒ S 2 − 8S − 1920 = 0 ⇒ (S − 48)(S + 40) = 0 ⇒ S = 48 km/hr [Since speed can't be negative] So, the original speed (S) is 48 km/hr Also, the time taken to cover 480 km = $\frac{480}{48}$ = 10 hr Hence, the correct answer is 10.
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