A man riding a bicycle covers distance of 36 km in the direction of wind and comes back to his original position in 8 hours. If the speed of the wind is 12 km/hr , find the speed of the bicycle .
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Sol: Let the speed of bicycle be x km / hr Speed of wind is 10 km /hr Speed of bicycle in the direction of wind = (x + 10) km/hr Speed of the bicycle against the direction of wind = (x – 10) km/hr Speed = Distance / Time Time = Distance / Speed Time taken by man when riding in the direction of wind = (60 / x+10) hrs Time taken by man when riding in the opposite direction of wind = (60 / x-10) hrs (60 / x +10) + (60 / x+10) = 8 60[(1 / x+10) + (1 / x-10)] = 8 [(1 / x+10) + (1 / x-10)] = 8/60 2x / x2 - 100 = 2 / 15 ⇒ x2 - 15x - 100 = 0 ⇒ (x + 5)(x - 20) = 0 ⇒ x = -5 or 20 Speed can never be negative. Hence x = 20. Therefore, the speed of the bicycle is 20 km/hr.
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