Advertisements
Advertisements
प्रश्न
A piece of equipment cost a certain factory Rs 600,000. 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?
उत्तर
Given: A piece of equipment cost a certain factory is 600,000
To find: Value of the equipment at the end of 10 years
It depreciates 15%, 13.5%, 12% in 1st, 2nd, 3rd year and so on.
This means the price of the equipment is depreciating in an A.P.
A.P. will be 15, 13.5, 12,…………………………up to 10 terms
Hence a = 15, d = 13.5 – 15 = –1.5
Formula used:
`S_n = n/2 {2a +(n-1)d}`
where a is first term, d is common difference and n is number of terms in an A.P.
Therefore,
Total percentage of depreciation in 10 years,
`S_10 =10/2{2xx15+(10-1)xx-1.5}`
⇒ S10 = 5(30+9× -1.5)
⇒ S10 = 5(30 -13.5 )
⇒ S10 = 5(16.5)
⇒ S10 = 82.5
Value of the equipment at the end of 10 years,
`= (100-"Depreciation"%)/100 xx "cost of equipment"`
`=(100-82.5)/100 xx 600000`
`= 175/10 xx 6000`
=175 × 600
= 105000
Hence, value of equipment at the end of 10 years is Rs. 105000
APPEARS IN
संबंधित प्रश्न
Find the sum to n terms of the A.P., whose kth term is 5k + 1.
Sum of the first p, q and r terms of an A.P. are a, b and c, respectively.
Prove that `a/p (q - r) + b/q (r- p) + c/r (p - q) = 0`
Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7th and (m – 1)th numbers is 5:9. Find the value of m.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
if `a(1/b + 1/c), b(1/c+1/a), c(1/a+1/b)` are in A.P., prove that a, b, c are in A.P.
A manufacturer reckons that the value of a machine, which costs him Rs 15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years.
A sequence is defined by an = n3 − 6n2 + 11n − 6, n ϵ N. Show that the first three terms of the sequence are zero and all other terms are positive.
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2}, 7\sqrt{2}, . . .\]
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
9, 7, 5, 3, ...
Find:
nth term of the A.P. 13, 8, 3, −2, ...
If the sequence < an > is an A.P., show that am +n +am − n = 2am.
Which term of the A.P. 4, 9, 14, ... is 254?
Is 302 a term of the A.P. 3, 8, 13, ...?
Which term of the sequence 12 + 8i, 11 + 6i, 10 + 4i, ... is purely imaginary?
The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.
The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.
Find the sum of the following arithmetic progression :
50, 46, 42, ... to 10 terms
Find the sum of the following serie:
101 + 99 + 97 + ... + 47
Find the sum of the following serie:
(a − b)2 + (a2 + b2) + (a + b)2 + ... + [(a + b)2 + 6ab]
Find the sum of all integers between 50 and 500 which are divisible by 7.
Find the sum of n terms of the A.P. whose kth terms is 5k + 1.
In an A.P. the first term is 2 and the sum of the first five terms is one fourth of the next five terms. Show that 20th term is −112.
A man saves Rs 32 during the first year. Rs 36 in the second year and in this way he increases his savings by Rs 4 every year. Find in what time his saving will be Rs 200.
A man arranges to pay off a debt of Rs 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of the debt unpaid, find the value of the first instalment.
A carpenter was hired to build 192 window frames. The first day he made five frames and each day thereafter he made two more frames than he made the day before. How many days did it take him to finish the job?
Write the sum of first n odd natural numbers.
Write the value of n for which n th terms of the A.P.s 3, 10, 17, ... and 63, 65, 67, .... are equal.
If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is
If Sn denotes the sum of first n terms of an A.P. < an > such that
If the sum of n terms of an A.P. is 2 n2 + 5 n, then its nth term is
If a1, a2, a3, .... an are in A.P. with common difference d, then the sum of the series sin d [cosec a1cosec a2 + cosec a1 cosec a3 + .... + cosec an − 1 cosec an] is
If the first, second and last term of an A.P are a, b and 2a respectively, then its sum is
In an A.P. the pth term is q and the (p + q)th term is 0. Then the qth term is ______.
The sum of terms equidistant from the beginning and end in an A.P. is equal to ______.
If the ratio of the sum of n terms of two APs is 2n:(n + 1), then the ratio of their 8th terms is ______.
If b2, a2, c2 are in A.P., then `1/(a + b), 1/(b + c), 1/(c + a)` will be in ______
