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Duration of a metro journey varies directly as the distance and inversely as the velocity. The velocity varies directly as the square root of the quantity of electricity used; and inversely as the number of carriages in the train. 100 units of electricity is required for the journey of 50 km in half an hour with 18 carriages. How much electricity will be consumed in a journey of 42 km in 28 minutes with 16 carriages?
- a)69 units
- b)65 units
- c)89 units
- d)64 units
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Duration of a metro journey varies directly as the distance and invers...
Where t is time, s is distance, v is velocity, Q is the amount of electricity used, n is the number of carriages and k1,k2 k care constants. Also, k = k1,k2
Hence, option 4.
Most Upvoted Answer
Duration of a metro journey varies directly as the distance and invers...
To solve this problem, we can break it down into smaller steps. Let's start by identifying the given information and the variables involved:
Given:
- Duration of the metro journey varies directly with the distance and inversely with the velocity.
- Velocity varies directly with the square root of the quantity of electricity used and inversely with the number of carriages in the train.
- A journey of 50 km in half an hour with 18 carriages requires 100 units of electricity.
Variables:
- Distance: d (in km)
- Duration: t (in minutes)
- Velocity: v (in units)
- Electricity used: e (in units)
- Number of carriages: c
Step 1: Determine the relationship between duration, distance, and velocity
Since the duration varies directly with the distance and inversely with the velocity, we can write the equation as:
t ∝ d/v
Step 2: Determine the relationship between velocity, electricity used, and number of carriages
Since the velocity varies directly with the square root of the electricity used and inversely with the number of carriages, we can write the equation as:
v ∝ √e/c
Step 3: Combine the two equations to solve for the variables
Substituting the equation from Step 2 into the equation from Step 1, we get:
t ∝ d/(√e/c)
Simplifying the equation, we get:
t ∝ d√(c/e)
Step 4: Use the given information to find the proportionality constant
We can use the given information about the journey of 50 km in half an hour with 18 carriages requiring 100 units of electricity to find the proportionality constant.
Using the formula t ∝ d√(c/e), we have:
0.5 ∝ 50√(18/100)
Simplifying the equation, we get:
0.5 ∝ 50√(9/50)
0.5 ∝ 50(3/5)
0.5 ∝ 30
Therefore, the proportionality constant is 30.
Step 5: Use the proportionality constant to solve for the electricity used in the new journey
Now that we have the proportionality constant, we can use it to find the electricity used in the journey of 42 km in 28 minutes with 16 carriages.
Using the formula t ∝ d√(c/e), we have:
28 ∝ 42√(16/e)
Simplifying the equation, we get:
28 ∝ 42√(4/e)
28 ∝ 84/√e
Using the proportionality constant of 30, we can write the equation as:
28 = 30(84/√e)
Simplifying the equation, we get:
28 = 2520/√e
Cross-multiplying and squaring both sides of the equation, we get:
784 = 2520/e
Simplifying the equation, we get:
e = 2520/784
e ≈ 3.214
Therefore, the electricity consumed in the journey of 42 km in 28 minutes with 16 carriages is approximately 3.214 units.
The correct answer is not provided in the options given.
Given:
- Duration of the metro journey varies directly with the distance and inversely with the velocity.
- Velocity varies directly with the square root of the quantity of electricity used and inversely with the number of carriages in the train.
- A journey of 50 km in half an hour with 18 carriages requires 100 units of electricity.
Variables:
- Distance: d (in km)
- Duration: t (in minutes)
- Velocity: v (in units)
- Electricity used: e (in units)
- Number of carriages: c
Step 1: Determine the relationship between duration, distance, and velocity
Since the duration varies directly with the distance and inversely with the velocity, we can write the equation as:
t ∝ d/v
Step 2: Determine the relationship between velocity, electricity used, and number of carriages
Since the velocity varies directly with the square root of the electricity used and inversely with the number of carriages, we can write the equation as:
v ∝ √e/c
Step 3: Combine the two equations to solve for the variables
Substituting the equation from Step 2 into the equation from Step 1, we get:
t ∝ d/(√e/c)
Simplifying the equation, we get:
t ∝ d√(c/e)
Step 4: Use the given information to find the proportionality constant
We can use the given information about the journey of 50 km in half an hour with 18 carriages requiring 100 units of electricity to find the proportionality constant.
Using the formula t ∝ d√(c/e), we have:
0.5 ∝ 50√(18/100)
Simplifying the equation, we get:
0.5 ∝ 50√(9/50)
0.5 ∝ 50(3/5)
0.5 ∝ 30
Therefore, the proportionality constant is 30.
Step 5: Use the proportionality constant to solve for the electricity used in the new journey
Now that we have the proportionality constant, we can use it to find the electricity used in the journey of 42 km in 28 minutes with 16 carriages.
Using the formula t ∝ d√(c/e), we have:
28 ∝ 42√(16/e)
Simplifying the equation, we get:
28 ∝ 42√(4/e)
28 ∝ 84/√e
Using the proportionality constant of 30, we can write the equation as:
28 = 30(84/√e)
Simplifying the equation, we get:
28 = 2520/√e
Cross-multiplying and squaring both sides of the equation, we get:
784 = 2520/e
Simplifying the equation, we get:
e = 2520/784
e ≈ 3.214
Therefore, the electricity consumed in the journey of 42 km in 28 minutes with 16 carriages is approximately 3.214 units.
The correct answer is not provided in the options given.
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Duration of a metro journey varies directly as the distance and inversely as the velocity. The velocity varies directly as the square root of the quantity of electricity used; and inversely as the number of carriages in the train. 100 units of electricity is required for the journey of 50 km in half an hour with 18 carriages. How much electricity will be consumed in a journey of 42 km in 28 minutes with 16 carriages?a)69 unitsb)65 unitsc)89 unitsd)64 unitsCorrect answer is option 'D'. Can you explain this answer?
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Duration of a metro journey varies directly as the distance and inversely as the velocity. The velocity varies directly as the square root of the quantity of electricity used; and inversely as the number of carriages in the train. 100 units of electricity is required for the journey of 50 km in half an hour with 18 carriages. How much electricity will be consumed in a journey of 42 km in 28 minutes with 16 carriages?a)69 unitsb)65 unitsc)89 unitsd)64 unitsCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Duration of a metro journey varies directly as the distance and inversely as the velocity. The velocity varies directly as the square root of the quantity of electricity used; and inversely as the number of carriages in the train. 100 units of electricity is required for the journey of 50 km in half an hour with 18 carriages. How much electricity will be consumed in a journey of 42 km in 28 minutes with 16 carriages?a)69 unitsb)65 unitsc)89 unitsd)64 unitsCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Duration of a metro journey varies directly as the distance and inversely as the velocity. The velocity varies directly as the square root of the quantity of electricity used; and inversely as the number of carriages in the train. 100 units of electricity is required for the journey of 50 km in half an hour with 18 carriages. How much electricity will be consumed in a journey of 42 km in 28 minutes with 16 carriages?a)69 unitsb)65 unitsc)89 unitsd)64 unitsCorrect answer is option 'D'. Can you explain this answer?.
Duration of a metro journey varies directly as the distance and inversely as the velocity. The velocity varies directly as the square root of the quantity of electricity used; and inversely as the number of carriages in the train. 100 units of electricity is required for the journey of 50 km in half an hour with 18 carriages. How much electricity will be consumed in a journey of 42 km in 28 minutes with 16 carriages?a)69 unitsb)65 unitsc)89 unitsd)64 unitsCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Duration of a metro journey varies directly as the distance and inversely as the velocity. The velocity varies directly as the square root of the quantity of electricity used; and inversely as the number of carriages in the train. 100 units of electricity is required for the journey of 50 km in half an hour with 18 carriages. How much electricity will be consumed in a journey of 42 km in 28 minutes with 16 carriages?a)69 unitsb)65 unitsc)89 unitsd)64 unitsCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Duration of a metro journey varies directly as the distance and inversely as the velocity. The velocity varies directly as the square root of the quantity of electricity used; and inversely as the number of carriages in the train. 100 units of electricity is required for the journey of 50 km in half an hour with 18 carriages. How much electricity will be consumed in a journey of 42 km in 28 minutes with 16 carriages?a)69 unitsb)65 unitsc)89 unitsd)64 unitsCorrect answer is option 'D'. Can you explain this answer?.
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Duration of a metro journey varies directly as the distance and inversely as the velocity. The velocity varies directly as the square root of the quantity of electricity used; and inversely as the number of carriages in the train. 100 units of electricity is required for the journey of 50 km in half an hour with 18 carriages. How much electricity will be consumed in a journey of 42 km in 28 minutes with 16 carriages?a)69 unitsb)65 unitsc)89 unitsd)64 unitsCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Duration of a metro journey varies directly as the distance and inversely as the velocity. The velocity varies directly as the square root of the quantity of electricity used; and inversely as the number of carriages in the train. 100 units of electricity is required for the journey of 50 km in half an hour with 18 carriages. How much electricity will be consumed in a journey of 42 km in 28 minutes with 16 carriages?a)69 unitsb)65 unitsc)89 unitsd)64 unitsCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Duration of a metro journey varies directly as the distance and inversely as the velocity. The velocity varies directly as the square root of the quantity of electricity used; and inversely as the number of carriages in the train. 100 units of electricity is required for the journey of 50 km in half an hour with 18 carriages. How much electricity will be consumed in a journey of 42 km in 28 minutes with 16 carriages?a)69 unitsb)65 unitsc)89 unitsd)64 unitsCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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