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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  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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 ๐‘ฃ+600000/๐’ฑ (b) 375/4 ๐‘ฃ+600000/๐’ฑ (c) 15/16 ๐‘ฃ^2+150000/๐’ฑ (d) 3/16 ๐‘ฃ+6000/๐’ฑ Given that If the fuel costs โ‚น 48 per hour at speed 16 km per hour and the fixed charges to run the train amount to โ‚น 1200 per hour. Now, Speed of train = ๐’— km/hr Thus, Time taken to cover 500 km = ๐ท๐‘–๐‘ ๐‘ก๐‘Ž๐‘›๐‘๐‘’/๐‘†๐‘๐‘’๐‘’๐‘‘ = ๐Ÿ“๐ŸŽ๐ŸŽ/๐’— hours Now, Total cost = Fixed Charges + Running Charges Fixed Charges Given that Fixed charges to run the train amount to โ‚น 1200 per hour. Thus, Fixed Charges for 1 hour = Rs 1200 Fixed Charges for ๐Ÿ“๐ŸŽ๐ŸŽ/๐’— hours = Rs 1200 ร— 500/๐‘ฃ = Rs ๐Ÿ”๐ŸŽ๐ŸŽ๐ŸŽ๐ŸŽ๐ŸŽ/๐’— Running Charges Given that fuel costs โ‚น 48 per hour at speed 16 km per hour From previous question Fuel cost per hour = k ร— (Speed of train)2 = ๐Ÿ‘/๐Ÿ๐Ÿ” ๐’—^๐Ÿ Now, Fuel cost for for ๐Ÿ“๐ŸŽ๐ŸŽ/๐’— hours = Rs ๐Ÿ‘/๐Ÿ๐Ÿ” ๐’—^๐Ÿ ร— 500/๐‘ฃ = Rs ๐Ÿ‘๐Ÿ•๐Ÿ“/๐Ÿ’ ๐’— Thus, Total cost = Fixed Charges + Running Charges = Rs ๐Ÿ‘๐Ÿ•๐Ÿ“/๐Ÿ’ ๐’— + ๐Ÿ”๐ŸŽ๐ŸŽ๐ŸŽ๐ŸŽ๐ŸŽ/๐’— So, the correct answer is (b)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.