Question : A man travels 404 kilometres, partly by train and steamer. He spends 10 hours more time on the steamer. If the speed of the steamer is 30 km/hr and the velocity of the train is 50 km/hr, how much distance does he cover by steamer?
Option 1: 407 km
Option 2: 509 km
Option 3: 610 km
Option 4: 339 km
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Correct Answer: 339 km
Solution :
Let the time spent on the train be $x$ hours
and the time spent on the steamer is $(x+10)$ hours.
So, the distances travelled by train and steamer are $50x$ km and $30(x+10)$ km, respectively.
According to the question,
$50x + 30(x+10) = 404$
$⇒ 80x = 104$
$⇒ x = \frac{104}{80}$ hours
Then, the time spent on the steamer is = ($\frac{104}{80}$ + 10) = $\frac{904}{80}$ hours
$\therefore$ The distance covered by him on the steamer is = ($\frac{904}{80}$ × 30) = 339 km
Hence, the correct answer is 339 km.
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