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The speed of a motorboat is to that of the current of water as 36 : 5. The boats goes along with the current in 5 hours 10 min. It will come back in 

(a) 5 hrs 50 min 

(b) 6 hrs 

(c) 6 hrs 50 min 

(d) 12 hrs 10 min

1 Answer

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Best answer

(c)  6 hrs 50 min

Let the speed of the motorboat be 36x km/hr and that of the current of water be 5x km/hr. 

Speed downstream = (36x + 5x) km/hr = 41x km/hr 

Speed upstream = (36x – 5x) km/hr = 31x km/hr 

Time taken to travel downstream = 5 hrs 10 min

\(5\frac{10}{60}\) hrs = \(\frac{31}{6}\) hrs

∴ Distance covered downstream = \(\big(41x\times\frac{31}6\big)\) km

⇒ Distance covered upstream =   \(\big(41x\times\frac{31}6\big)\) km

∴ Time taken to travel upstream = \(\big(41x\times\frac{31}6\times\frac1{31x}\big)\) hrs

\(\frac{41}{6}\) hrs = \(6\frac56\) hrs = 6 hrs 50 min.

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