If the train has travelled a distance of 500 km, then the total cost of running the train is given by function:

(a) 15/16 v + 600000/V        (b) 375/4 v + 600000/V

(c) 15/16 v 2 + 150000/V    (d) 3/16 v + 6000/V

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Transcript

Question 47 If the train has travelled a distance of 500 km, then the total cost of running the train is given by function: (a) 15/16 𝑣+600000/𝒱 (b) 375/4 𝑣+600000/𝒱 (c) 15/16 𝑣^2+150000/𝒱 (d) 3/16 𝑣+6000/𝒱 Given that If the fuel costs ₹ 48 per hour at speed 16 km per hour and the fixed charges to run the train amount to ₹ 1200 per hour. Now, Speed of train = 𝒗 km/hr Thus, Time taken to cover 500 km = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒/𝑆𝑝𝑒𝑒𝑑 = 𝟓𝟎𝟎/𝒗 hours Now, Total cost = Fixed Charges + Running Charges Fixed Charges Given that Fixed charges to run the train amount to ₹ 1200 per hour. Thus, Fixed Charges for 1 hour = Rs 1200 Fixed Charges for 𝟓𝟎𝟎/𝒗 hours = Rs 1200 × 500/𝑣 = Rs 𝟔𝟎𝟎𝟎𝟎𝟎/𝒗 Running Charges Given that fuel costs ₹ 48 per hour at speed 16 km per hour From previous question Fuel cost per hour = k × (Speed of train)2 = 𝟑/𝟏𝟔 𝒗^𝟐 Now, Fuel cost for for 𝟓𝟎𝟎/𝒗 hours = Rs 𝟑/𝟏𝟔 𝒗^𝟐 × 500/𝑣 = Rs 𝟑𝟕𝟓/𝟒 𝒗 Thus, Total cost = Fixed Charges + Running Charges = Rs 𝟑𝟕𝟓/𝟒 𝒗 + 𝟔𝟎𝟎𝟎𝟎𝟎/𝒗 So, the correct answer is (b)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.