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
Check whether -150 is a term of the A.P. 11, 8, 5, 2, ....
In an AP given a = 3, n = 8, Sn = 192, find d.
A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.
Find the sum of all odd numbers between 100 and 200.
Find the sum of all even integers between 101 and 999.
Determine the A.P. Whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
If the 8th term of an A.P. is 37 and the 15th term is 15 more than the 12th term, find the A.P. Also, find the sum of first 20 terms of A.P.
Find the sum of all multiples of 7 lying between 300 and 700.
How many numbers are there between 101 and 999, which are divisible by both 2 and 5?
Find the value of x for which the numbers (5x + 2), (4x - 1) and (x + 2) are in AP.
The sum of three numbers in AP is 3 and their product is -35. Find the numbers.
Find the sum of n terms of the series \[\left( 4 - \frac{1}{n} \right) + \left( 4 - \frac{2}{n} \right) + \left( 4 - \frac{3}{n} \right) + . . . . . . . . . .\]
If Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to
If 18, a, b, −3 are in A.P., the a + b =
Q.7
Find the value of x, when in the A.P. given below 2 + 6 + 10 + ... + x = 1800.
The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.
The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 equal to the sum of first 2n terms of another A.P. whose first term is – 30 and the common difference is 8. Find n.
The sum of the 4th and 8th term of an A.P. is 24 and the sum of the 6th and 10th term of the A.P. is 44. Find the A.P. Also, find the sum of first 25 terms of the A.P.
