UPSC Exam > UPSC Questions > A machine depreciate at 10% of it's value at ...
Start Learning for Free
A machine depreciate at 10% of it's value at the beginning of a year. The cost and scrap value realized at the time of sale being ₹23240 and₹9000 respectively. for how many years the machine was put to use?
Most Upvoted Answer
A machine depreciate at 10% of it's value at the beginning of a year. ...
The problem of depreciation can be solved using the formula for the value of an asset after a certain number of years, taking into account its depreciation rate.
Understanding Depreciation
Depreciation is the reduction in the value of an asset over time. For this machine, it depreciates at a constant rate of 10% per year. The formula for the value of the machine after 'n' years can be expressed as:
Given Values
- Initial Cost = ₹23240
- Scrap Value = ₹9000
- Depreciation Rate = 10% or 0.10
Setting Up the Equation
To find out for how many years the machine was in use, we set up the equation:
Solving for n
1. Dividing both sides by ₹23240 gives:
2. Taking the logarithm of both sides:
3. Calculating the values:
Thus, the machine was used for approximately 6.56 years, which we can round to 7 years for practical purposes.
Conclusion
The machine was effectively put to use for about 7 years before reaching its scrap value.
Understanding Depreciation
Depreciation is the reduction in the value of an asset over time. For this machine, it depreciates at a constant rate of 10% per year. The formula for the value of the machine after 'n' years can be expressed as:
- Value after n years = Initial Cost × (1 - Depreciation Rate)n
Given Values
- Initial Cost = ₹23240
- Scrap Value = ₹9000
- Depreciation Rate = 10% or 0.10
Setting Up the Equation
To find out for how many years the machine was in use, we set up the equation:
- Scrap Value = Initial Cost × (1 - 0.10)n
- ₹9000 = ₹23240 × (0.90)n
Solving for n
1. Dividing both sides by ₹23240 gives:
- (0.90)n = ₹9000 / ₹23240
- (0.90)n ≈ 0.387
2. Taking the logarithm of both sides:
- n × log(0.90) = log(0.387)
- n = log(0.387) / log(0.90)
3. Calculating the values:
- n ≈ 6.56
Thus, the machine was used for approximately 6.56 years, which we can round to 7 years for practical purposes.
Conclusion
The machine was effectively put to use for about 7 years before reaching its scrap value.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
A machine depreciate at 10% of it's value at the beginning of a year. The cost and scrap value realized at the time of sale being ₹23240 and₹9000 respectively. for how many years the machine was put to use?
Question Description
A machine depreciate at 10% of it's value at the beginning of a year. The cost and scrap value realized at the time of sale being ₹23240 and₹9000 respectively. for how many years the machine was put to use? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A machine depreciate at 10% of it's value at the beginning of a year. The cost and scrap value realized at the time of sale being ₹23240 and₹9000 respectively. for how many years the machine was put to use? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A machine depreciate at 10% of it's value at the beginning of a year. The cost and scrap value realized at the time of sale being ₹23240 and₹9000 respectively. for how many years the machine was put to use?.
A machine depreciate at 10% of it's value at the beginning of a year. The cost and scrap value realized at the time of sale being ₹23240 and₹9000 respectively. for how many years the machine was put to use? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A machine depreciate at 10% of it's value at the beginning of a year. The cost and scrap value realized at the time of sale being ₹23240 and₹9000 respectively. for how many years the machine was put to use? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A machine depreciate at 10% of it's value at the beginning of a year. The cost and scrap value realized at the time of sale being ₹23240 and₹9000 respectively. for how many years the machine was put to use?.
Solutions for A machine depreciate at 10% of it's value at the beginning of a year. The cost and scrap value realized at the time of sale being ₹23240 and₹9000 respectively. for how many years the machine was put to use? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of A machine depreciate at 10% of it's value at the beginning of a year. The cost and scrap value realized at the time of sale being ₹23240 and₹9000 respectively. for how many years the machine was put to use? defined & explained in the simplest way possible. Besides giving the explanation of
A machine depreciate at 10% of it's value at the beginning of a year. The cost and scrap value realized at the time of sale being ₹23240 and₹9000 respectively. for how many years the machine was put to use?, a detailed solution for A machine depreciate at 10% of it's value at the beginning of a year. The cost and scrap value realized at the time of sale being ₹23240 and₹9000 respectively. for how many years the machine was put to use? has been provided alongside types of A machine depreciate at 10% of it's value at the beginning of a year. The cost and scrap value realized at the time of sale being ₹23240 and₹9000 respectively. for how many years the machine was put to use? theory, EduRev gives you an
ample number of questions to practice A machine depreciate at 10% of it's value at the beginning of a year. The cost and scrap value realized at the time of sale being ₹23240 and₹9000 respectively. for how many years the machine was put to use? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup