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Mitul goes out to shop on a snowy day. He travels at a speed of a km/hr when it’s snowing and at a speed of (a – 1) km/hr when it stops snowing. If his average speed for the journey is 6.4 km/hr. Find the fraction of the distance which he covered while it was snowing. Given, that a is an integer.1. 7/152. 7/163. 1/44. 3/55. None of the above |
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Answer» Correct Answer - Option 2 : 7/16 Calculation: Let the time for which he traveled in snow be ‘x’ hr and time for which he travelled when it stopped snowing be ‘y’ hr. Given, Mitul travels at a speed of a km/hr when it’s snowing and at a speed of (a – 1) km/hr when it stops snowing. Average speed = 6.4 km/hr ⇒ Thus, a > 6.4 > a – 1 ⇒ a > 6.4 or a < 7.4 ∴ As n is an integer, a = 7 km/hr. Now, Mitul travels at a speed of 7 km/hr when it’s snowing and at a speed of 6 km/hr when it’s not snowing. ∴ Total distance traveled = 7x + 6y Total time taken = x + y ⇒ (7x + 6y)/x + y = 6.4 ⇒ 7x + 6y = 6.4x + 6.4y ⇒ 0.6x = 0.4y ⇒ y = 1.5x ∴ Total distance traveled = 7x + 9x = 16x ∴ Fraction of distance traveled in the snow = 7x/16x ⇒ 7/16 The fraction of the distance which he covered while it was snowing is 7/16. |
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