Question 47 (Case Based Question) - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by Teachoo

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

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)

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.

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