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The time taken to travel from Mumbai to Pune varies directly as the distance and inversely as the velocity of the train. The velocity varies directly as the square root of the number of units of electricity used per km and inversely as the number of coaches attached to the engine. It takes three hours to reach Pune when 15 coaches are attached to the engine and 2025 units of electricity are utilized per km. What should be the number of electricity units utilized per km in order to reach Pune in the same time if 20 coaches are attached to the engine?
- a)2500
- b)3025
- c)3600
- d)Data inadequate
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The time taken to travel from Mumbai to Pune varies directly as the di...
Let t be the time taken, d be the distance, TV be the number of coaches and U be the number of electricity units utilized per km. Let k be the constant of proportionality.
In the first case
Now, in the second case, N= 20 and t = 3
Hence, option 3.
Most Upvoted Answer
The time taken to travel from Mumbai to Pune varies directly as the di...
To solve this problem, we need to find the relationship between the time taken to travel from Mumbai to Pune and the number of electricity units utilized per km. Let's break down the problem step by step:
Step 1: Define the variables
Let:
- T be the time taken to travel from Mumbai to Pune (in hours)
- D be the distance between Mumbai and Pune (in km)
- V be the velocity of the train (in km/h)
- E be the number of electricity units utilized per km
- C be the number of coaches attached to the engine
Step 2: Establish the direct and inverse relationships
According to the problem statement:
- The time taken to travel varies directly as the distance and inversely as the velocity, so we can write:
T ∝ D/V
- The velocity varies directly as the square root of the number of electricity units utilized per km and inversely as the number of coaches attached to the engine, so we can write:
V ∝ √E/C
Step 3: Combine the relationships
Combining the two relationships, we get:
T ∝ D/(√E/C)
Step 4: Solve the problem
Given that it takes 3 hours to reach Pune when 15 coaches are attached to the engine and 2025 units of electricity are utilized per km, we can substitute the values into the equation:
3 ∝ D/(√2025/15)
Simplifying the equation:
3 ∝ D/(√135)
To find the number of electricity units utilized per km in order to reach Pune in the same time with 20 coaches attached to the engine, we need to find the value of E that satisfies the equation:
3 ∝ D/(√E/20)
Since the time taken to travel remains the same, we can set up the equation:
D/(√2025/15) = D/(√E/20)
Simplifying the equation:
√E/20 = √2025/15
Cross-multiplying:
15√E = 20√2025
Simplifying further:
√E = (20√2025)/15
Squaring both sides to eliminate the square root:
E = [(20√2025)/15]^2
Calculating the value:
E = (20/15)^2 * 45
E = 4/3 * 45
E = 60
Therefore, the number of electricity units utilized per km in order to reach Pune in the same time with 20 coaches attached to the engine should be 60 units.
Hence, the correct answer is option C) 3600.
Step 1: Define the variables
Let:
- T be the time taken to travel from Mumbai to Pune (in hours)
- D be the distance between Mumbai and Pune (in km)
- V be the velocity of the train (in km/h)
- E be the number of electricity units utilized per km
- C be the number of coaches attached to the engine
Step 2: Establish the direct and inverse relationships
According to the problem statement:
- The time taken to travel varies directly as the distance and inversely as the velocity, so we can write:
T ∝ D/V
- The velocity varies directly as the square root of the number of electricity units utilized per km and inversely as the number of coaches attached to the engine, so we can write:
V ∝ √E/C
Step 3: Combine the relationships
Combining the two relationships, we get:
T ∝ D/(√E/C)
Step 4: Solve the problem
Given that it takes 3 hours to reach Pune when 15 coaches are attached to the engine and 2025 units of electricity are utilized per km, we can substitute the values into the equation:
3 ∝ D/(√2025/15)
Simplifying the equation:
3 ∝ D/(√135)
To find the number of electricity units utilized per km in order to reach Pune in the same time with 20 coaches attached to the engine, we need to find the value of E that satisfies the equation:
3 ∝ D/(√E/20)
Since the time taken to travel remains the same, we can set up the equation:
D/(√2025/15) = D/(√E/20)
Simplifying the equation:
√E/20 = √2025/15
Cross-multiplying:
15√E = 20√2025
Simplifying further:
√E = (20√2025)/15
Squaring both sides to eliminate the square root:
E = [(20√2025)/15]^2
Calculating the value:
E = (20/15)^2 * 45
E = 4/3 * 45
E = 60
Therefore, the number of electricity units utilized per km in order to reach Pune in the same time with 20 coaches attached to the engine should be 60 units.
Hence, the correct answer is option C) 3600.
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The time taken to travel from Mumbai to Pune varies directly as the distance and inversely as the velocity of the train. The velocity varies directly as the square root of the number of units of electricity used per km and inversely as the number of coaches attached to the engine. It takes three hours to reach Pune when 15 coaches are attached to the engine and 2025 units of electricity are utilized per km. What should be the number of electricity units utilized per km in order to reach Pune in the same time if 20 coaches are attached to the engine?a)2500b)3025c)3600d)Data inadequateCorrect answer is option 'C'. Can you explain this answer?
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