The total time taken by a boat to cover a certain distance in downstream and the same distance in upstream is 10 hours. The same boat can cover 1200 km distance in still water in (t-1) hour. The speed of boat in still water is 2.5 times of the speed of stream.

Which of the following statements is/are correct?

(i) If ‘t’ = 7, then the speed of the boat in still water will be 200 km/h.

(ii) If the speed of boat in still water is 250 km/h, then the distance covered by the boat in downstream and upstream will be the multiple of 3. 

(iii) If the speed of stream is 60 km/h, then the value of ‘t’ will be 8.

Solution

Let’s assume the speed of boat in still water and the speed of stream are ‘B’ and ‘C’ respectively.

The speed of boat in still water is 2.5 times of the speed of stream.

B = 2.5C    Eq.(i)

The same boat can cover 1200 km distance in still water in (t-1) hour. 

1200/B = (t-1)

Put Eq.(i) in the above equation.

1200/2.5C = (t-1)

480/C = (t-1)    Eq.(ii)

The total time taken by a boat to cover a certain distance in downstream and the same distance in upstream is 10 hours.

Let’s assume the distance covered in each of the stream is ‘d’.

[d/(B+C)] + [d/(B-C)] = 10

Put Eq.(i) in the above equation.

[d/(2.5C+C)] + [d/(2.5C-C)] = 10

[d/3.5C] + [d/1.5C] = 10    Eq.(iii)

(i) If ‘t’ = 7, then the speed of the boat in still water will be 200 km/h.

480/C = (7-1)

480/C = 6

C = 80 km/h

B = 2.5C = 2.5x80 = 200 km/h

So the given statement is correct.

(ii) If the speed of boat in still water is 250 km/h, then the distance covered by the boat in downstream and upstream will be the multiple of 3.

B = 2.5C

250 = 2.5C

C = 100 km/h

[d/3.5x100] + [d/1.5x100] = 10

[d/350] + [d/150] = 10

[50d/5250] = 10

d/105 = 10

d = 1050

So the given statement is correct.

(iii) If the speed of stream is 60 km/h, then the value of ‘t’ will be 8.

480/60 = (t-1)

(t-1) = 8

Here t = 8+1 = 9.

So the given statement is not correct.