boat can cover a distance of 7.2 km downstream and 3.2 km upstream in 2 hours. It can also cover 1.5 km downstream and 0.6 km upstream in 24 minutes. What is the speed of the boat when going downstream (in km/h) ? नाव धारा के अनुकूल 7.2 किमी और धारा के प्रतिकूल 3.2 किमी की दूरी 2 घंटे में तय कर सकती है। यह 1.5 किमी अनुकूल और 0.6 किमी प्रतिकूल 24 मिनट में तय कर सकती है। धारा के अनुकूल जाते समय नाव की गति (किमी/घंटा में) क्या है?

Let boat speed in still water be b and stream speed be c. Downstream speed = b + c, upstream = b - c. First condition: 7.2/(b+c) + 3.2/(b-c) = 2 hours. Second condition (24 min = 0.4 hours): 1.5/(b+c) + 0.6/(b-c) = 0.4. Multiply second by 4: 6/(b+c) + 2.4/(b-c) = 1.6. Notice this is close to the first equation. Subtract: (7.2-6)/(b+c) + (3.2-2.4)/(b-c) = 2-1.6, so 1.2/(b+c) + 0.8/(b-c) = 0.4. Multiply by 5: 6/(b+c) + 4/(b-c) = 2. From original second equation (×10): 15/(b+c) + 6/(b-c) = 4. Solve: Let x = 1/(b+c), y = 1/(b-c). We have 15x + 6y = 4 and 6x + 4y = 2. From second: 3x + 2y = 1, so y = (1-3x)/2. Substituting: 15x + 6(1-3x)/2 = 4, so 15x + 3 - 9x = 4, giving 6x = 1, x = 1/6. Therefore b + c = 6 km/h. Option B (4.5) would be if we miscalculated the relationship.