Speed of a ship is 6 m/s, which increases by 2 m/s after every 5 minutes. It travels upstream for 15 minutes and then travels downstream for 15 minutes. If speed of stream is 2 m/s and difference between the upstream distance travelled and the downstream distance travelled by the ship is ‘5k’ metres, then find the sum of squares of each digit of ‘k’. 

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