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?
Advertisements
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
संबंधित प्रश्न
Find the sum of odd integers from 1 to 2001.
If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.
Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual installment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?
Which term of the A.P. 3, 8, 13, ... is 248?
Which term of the A.P. 84, 80, 76,... is 0?
Is 302 a term of the A.P. 3, 8, 13, ...?
Which term of the sequence 24, \[23\frac{1}{4,} 22\frac{1}{2,} 21\frac{3}{4}\]....... is the first negative term?
How many terms are there in the A.P. 7, 10, 13, ... 43 ?
An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.
How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?
Find the sum of the following arithmetic progression :
3, 9/2, 6, 15/2, ... to 25 terms
Find the sum of the following arithmetic progression :
a + b, a − b, a − 3b, ... to 22 terms
Find the sum of all integers between 84 and 719, which are multiples of 5.
Find the sum of all integers between 100 and 550, which are divisible by 9.
Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.
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.
The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th terms.
If a, b, c is in A.P., then show that:
a2 (b + c), b2 (c + a), c2 (a + b) are also in A.P.
If a, b, c is in A.P., then show that:
b + c − a, c + a − b, a + b − c are in A.P.
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.
The income of a person is Rs 300,000 in the first year and he receives an increase of Rs 10000 to his income per year for the next 19 years. Find the total amount, he received in 20 years.
Write the common difference of an A.P. whose nth term is xn + y.
If the sums of n terms of two arithmetic progressions are in the ratio 2n + 5 : 3n + 4, then write the ratio of their m th terms.
If \[\frac{3 + 5 + 7 + . . . + \text { upto n terms }}{5 + 8 + 11 + . . . . \text { upto 10 terms }}\] 7, then find the value of n.
If the sums of n terms of two AP.'s are in the ratio (3n + 2) : (2n + 3), then find the ratio of their 12th terms.
If the sum of n terms of an A.P. be 3 n2 − n and its common difference is 6, then its first term is
In the arithmetic progression whose common difference is non-zero, the sum of first 3 n terms is equal to the sum of next n terms. Then the ratio of the sum of the first 2 n terms to the next 2 nterms is
If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are
If, S1 is the sum of an arithmetic progression of 'n' odd number of terms and S2 the sum of the terms of the series in odd places, then \[\frac{S_1}{S_2}\] =
If second, third and sixth terms of an A.P. are consecutive terms of a G.P., write the common ratio of the G.P.
The first three of four given numbers are in G.P. and their last three are in A.P. with common difference 6. If first and fourth numbers are equal, then the first number is
Find the rth term of an A.P. sum of whose first n terms is 2n + 3n2
If the sum of n terms of an A.P. is given by Sn = 3n + 2n2, then the common difference of the A.P. is ______.
Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.
If 100 times the 100th term of an A.P. with non zero common difference equals the 50 times its 50th term, then the 150th term of this A.P. is ______.
