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Question

A boat goes 80 km upstream and 120 km downstream in 20 hours. In 15 hours, it can go 48 km upstream and 108 km down-stream. Determine the speed of the boat in still water and that of the stream. [4 MARKS]

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Solution

Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

Let speed of boat in still water be x km/hr and speed of stream be y km/hr

Hence speed of upstream =xy

Speed downstream =x+y

Time taken to cover 80 km upstream =80xy

Time taken to cover 120 km downstream =120x+y

Total time taken is = 20 hrs

80xy+120x+y=20

80u+120v=20 where 1xy=u,1x+y=v

4u+6v=1(i)

Similarly,

48xy+108x+y=15

48u+108v=15

16u+36v=5(ii)

Solving (i) and (i) we get,

4u+6v=1u=16v4

Substituting value of u in (ii)

16u+36v=5

16(16v4)+36v=5

424v+36v=5

v=112

Now, u=16v4

u=18

v=1121x+y=112

x+y=12(iii)

u=181xy=18

xy=8(iv)

Solving (iii) and (iv) we get,

x=10,y=2

Speed of boat in still water is 10 km/hr

And speed of stream 2 km/hr


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