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The total profit made by running a train between New Delhi to Lucknow consists of two parts: (i) a constant amount of Rs 24 lakh per trip and (ii) it varies as the square of the number of coaches attached to the engine that amounts to Rs 7P2, where P is the number of coaches attached to the engine in the trip. If the average profit per coach per trip should not fall below Rs 169 lakh, then what is the minimum number of coaches that have to be attached to the engine?
- a)23
- b)24
- c)25
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The total profit made by running a train between New Delhi to Lucknow ...
Total profit = Rs 24 L + Rs 7P2, where P is the number of coaches.
which must be at least 169P
so now we get the equation
169P = 24L + 7P2 or 7P2- 169P + 24 = 0
on solving we get P = 24
Now go through the options.
which must be at least 169P
so now we get the equation
169P = 24L + 7P2 or 7P2- 169P + 24 = 0
on solving we get P = 24
Now go through the options.
Most Upvoted Answer
The total profit made by running a train between New Delhi to Lucknow ...
Total profit is 24L+7P^2 which must be at least 169*P. So now we get the equation
169P=24L+7P^2
or
7P^2-169P+24=0
On solving this we get P=24
169P=24L+7P^2
or
7P^2-169P+24=0
On solving this we get P=24
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Community Answer
The total profit made by running a train between New Delhi to Lucknow ...
Given, the total profit made by running a train between New Delhi to Lucknow consists of two parts:
(i) a constant amount of Rs 24 lakh per trip
(ii) it varies as the square of the number of coaches attached to the engine that amounts to Rs 7P2, where P is the number of coaches attached to the engine in the trip.
Let's assume that 'n' is the number of coaches attached to the engine in the trip.
According to the question,
Total profit = Rs 24 lakh + Rs 7n^2
Average profit per coach per trip = (Total profit) / (Number of coaches)
=> 169 = [24 + 7n^2] / n
On solving the above equation, we get n = 24.09
Since the number of coaches must be a whole number, the minimum number of coaches that have to be attached to the engine = 24.
Therefore, the correct answer is option B) 24.
(i) a constant amount of Rs 24 lakh per trip
(ii) it varies as the square of the number of coaches attached to the engine that amounts to Rs 7P2, where P is the number of coaches attached to the engine in the trip.
Let's assume that 'n' is the number of coaches attached to the engine in the trip.
According to the question,
Total profit = Rs 24 lakh + Rs 7n^2
Average profit per coach per trip = (Total profit) / (Number of coaches)
=> 169 = [24 + 7n^2] / n
On solving the above equation, we get n = 24.09
Since the number of coaches must be a whole number, the minimum number of coaches that have to be attached to the engine = 24.
Therefore, the correct answer is option B) 24.
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The total profit made by running a train between New Delhi to Lucknow consists of two parts: (i) a constant amount of Rs 24 lakh per trip and (ii) it varies as the square of the number of coaches attached to the engine that amounts to Rs 7P2, where P is the number of coaches attached to the engine in the trip. If the average profit per coach per trip should not fall below Rs 169 lakh, then what is the minimum number of coaches that have to be attached to the engine?a)23b)24c)25d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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