Advertisements
Advertisements
Question
A piece of equipment cost a certain factory Rs 60,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?
Advertisements
Solution
In the given problem,
Cost of the equipment = Rs 600,000
It depreciates by 15% in the first year. So,
Depreciation in 1 year
= 600000 − 495000
= 105000
= 90000
It depreciates by 13.5% of the original cost in the 2 year. So,
Depreciation in 2 year `= (13.5)/100 (600000) = 81000`
Further, it depreciates by 12% of the original cost in the 3 year. So,
Depreciation in 3 year `= 12/100 (600000)=72000`
So, the depreciation in value of the equipment forms an A.P. with first term as 90000 and common difference as −9000.
So, the total depreciation in value in 10 years can be calculated by using the formula for the sum of n terms of an A.P.
`S_n = n/2 [2a + (n-1) d]`
We get,
`S_n = 10/2 [2(90000) +(10-1)(-9000)]`
`=10/2 [180000 + (9)(-9000)]`
`=5(180000 - 81000)`
` = 5(99000)`
= 495000
So, the total depreciation in the value after 10 years is Rs 495000.
Therefore, the value of equipment = 600000 − 495000 = 105000
So, the value of the equipment after 10 years is Rs 105,000.
APPEARS IN
RELATED QUESTIONS
The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
If the term of m terms of an A.P. is the same as the sum of its n terms, show that the sum of its (m + n) terms is zero
In an AP, given a = 7, a13 = 35, find d and S13.
Find how many integers between 200 and 500 are divisible by 8.
The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?
If the 10th term of an AP is 52 and 17th term is 20 more than its 13th term, find the AP
Is -150 a term of the AP 11, 8, 5, 2, ……?
A sum of ₹2800 is to be used to award four prizes. If each prize after the first is ₹200 less than the preceding prize, find the value of each of the prizes
If (2p +1), 13, (5p -3) are in AP, find the value of p.
If the ratio of sum of the first m and n terms of an AP is m2 : n2, show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1) ?
Find out the sum of all natural numbers between 1 and 145 which are divisible by 4.
Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − kSn−1 + Sn−2, then k =
A sum of Rs. 700 is to be paid to give seven cash prizes to the students of a school for their overall academic performance. If the cost of each prize is Rs. 20 less than its preceding prize; find the value of each of the prizes.
If the sum of first n terms of an AP is An + Bn² where A and B are constants. The common difference of AP will be ______.
Find the sum of 12 terms of an A.P. whose nth term is given by an = 3n + 4.
Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.
[Hint (iii) : These numbers will be : multiples of 2 + multiples of 5 – multiples of 2 as well as of 5]
Find the sum:
1 + (–2) + (–5) + (–8) + ... + (–236)
Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?
The ratio of the 11th term to the 18th term of an AP is 2 : 3. Find the ratio of the 5th term to the 21st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.
