Speed of a ship is 6 m/s, which increases by 2 m/s after

Solution

Upstream speed of ship in first 5 minutes = 6 − 2 = 4 m/s Upstream distance covered by ship in first 5 minutes = 4 × 5 × 60 = 1200 metres Upstream speed of ship in next 5 minutes = (6 + 2) − 2 = 6 m/s Upstream distance covered by ship in next 5 minutes = 6 × 5 × 60 = 1800 metres Upstream speed of ship in next 5 minutes = (8 + 2) − 2 = 8 m/s Upstream distance covered by ship in next 5 minutes = 8 × 5 × 60 = 2400 metres Overall upstream distance covered by the ship: = 1200 + 1800 + 2400 = 5400 metres Downstream speed of ship in first 5 minutes = (10 + 2) + 2 = 14 m/s Downstream distance covered by ship in first 5 minutes = 14 × 5 × 60 = 4200 metres Downstream speed of ship in next 5 minutes = (12 + 2) + 2 = 16 m/s Downstream distance covered by ship in next 5 minutes = 16 × 5 × 60 = 4800 metres Downstream speed of ship in next 5 minutes = (14 + 2) + 2 = 18 m/s Downstream distance covered by ship in next 5 minutes = 18 × 5 × 60 = 5400 metres Overall downstream distance covered by the ship: = 4200 + 4800 + 5400 = 14400 metres So, 5k = 14400 − 5400 Or, 5k = 9000 Or, k = 1800 Required sum = 1² + 8² + 0² + 0² = 1 + 64 + 0 + 0 = 65