A motorboat whose speed is 27 km/h in still water takes 20 minutes more to go 40 km upstream than to

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04 Aug 2022 Boat and Streams

A motorboat whose speed is 27 km/h in still water takes 20 minutes more to go 40 km upstream than to cover the same distance downstream. If the speed of the boat in still water is increased by 3 km/h, then how much time will it take to go 44 km downstream and 54 km upstream ?

OPtion

1) 3 hours 16 minutes
2) 4 hours 20 minutes
3) 6 hours 24 minutes
4) 4 hours 40 minutes
5) 6 hours 40 minutes
6) 1 hours 20 minutes
7) 2 hours 20 minutes
8) 3 hours 20 minutes
9) 2 hours 40 minutes
10) None of these

Solution

Let speed of the stream=x km/h, then Downstream speed=(27+x) km/h and Upstream speed=(27-x) km/h
Difference of time for 40 km upstream & downstream = 40/(27-x) - 40/(27+x) = 1/3 hrs.
⇒ x² + 240x - 729 = 0
(x+243) (x-3) = 0
x=3 km/h
Now, new speed of a boat in still water=27+3=30 km/h
.'. Downstream speed=(30+3)=33 km/h, Upstream speed=(30-3)=27 km/h
Hence, time required for 44 km downstream and 54 km upstream = (44/33) + (54/27) hrs = 10/3 hrs = 3 hrs 20 min.
Correct Option 8)

Correct Option: 8 Best Solution (1)

Dr.Dipin Singh   1 year AGO

If x is speed of stream, then
40/ (27-x) - (40/(27+x) = 1/3
x= 3 kmph
Time reqd for given distances = 44/33+54/27= 3 1/3 hrs

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