Solution

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

A boat can cover ‘y’ km distance downstream in (t+2.5) hours.

(B+C) = y/(t+2.5)

y/(B+C) = (t+2.5)    Eq.(i)

The same boat can cover ‘0.25y’ km distance upstream in ‘t’ hours.

(B-C) = 0.25y/t

0.25y/(B-C) = t

y/[4(B-C)] = t

y/(B-C) = 4t    Eq.(ii)

If the total time taken by the boat to cover ‘y’ km distance downstream and the same distance upstream is 65 hours.

(y/(B+C))+(y/(B-C)) = 65

Put Eq.(i) and Eq.(ii) in the above equation.

(t+2.5)+4t = 65

5t+2.5 = 65

5t = 65-2.5

5t = 62.5

t = 12.5    Eq.(iii)

The time taken by the boat to cover 728 km in still water is (2t+3) hours.

728/B = (2t+3)

Put the value of ‘t’ from Eq.(iii) in the above equation.

728/B = (2x12.5+3)

728/B = (25+3)

728/B = 28

728/28 = B

B = 26    Eq.(iv)

Put the value of ‘B’ and ‘t’ in Eq.(i) and Eq.(ii).

y/(26+C) = (12.5+2.5)

y = 15(26+C)    Eq.(v)

y/(26-C) = 4x12.5

y/(26-C) = 50

y = 50(26-C)    Eq.(vi)

Equating Eq.(v) Eq.(vi).

15(26+C) = 50(26-C)

3(26+C) = 10(26-C)

78+3C = 260-10C

13C = 260-78

13C = 182

C = 14

So the speed of the stream = 14 km/h