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A boat with a speed of 21 km/hr in still water, travels from point A to B in the downstream direction and returns to point A. Another boat with speed of 28 km/hr travels from B to A and returns to point B. The difference between the time taken by them to cover the distance is 6.5 hrs. What is the distance between points A and B, if the speed of stream is 7 km/hr?
1. 420 km
2. 120 km
3. 280 km
4. 350 km
5. 210 km

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Correct Answer - Option 5 : 210 km

Speed of first boat from point A to B in downsream direction = 21 + 7 = 28 km/hr

Speed of first boat from point B to A(upstream) = 21 – 7 = 14 km/hr

Let the distance between A to B = D

Total time taken to complete this distance by first boat

⇒ (D/28) + (D/14) = 3D/28

Speed of second boat from point B to A in upstream direction = 28 – 7 = 21 km/hr

Speed of second boat from point A to B(downstream) = 28 + 7 = 35 km/hr

Total time taken to complete this distance by second boat

⇒ (D/21) + (D/35) = 8D/105

According to question,

(3D/28) – (8D/105) = 6.5

⇒ (45D – 32D)/420 = 6.5

⇒ D = 210

∴ The distance between points A and B is 210 km

 

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