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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