Advertisements
Advertisements
Question
The population of a suburb is 16000. Find the rate of increase in the population if the population after two years is 17640.
Advertisements
Solution
Here, P = Population of a suburb = 16000
A = Population after two years =17640
R = R %
N = 2 years
A = P `(1 + "R"/100)^"N"`
= 17640 = 16000 `(1 + "R"/100)^2`
= `17640/16000` = `(1 + "R"/100)^2`
= `441/400` = `(1 + "R"/100)^2`
Taking square roots from both
= `(1 + "R"/100) = _-^+(21/20)`
= `"R"/100` = `21/20`
= `"R"/100 = _-^+ 21/20 - 1`
= `"R" /100 (+ 21/20-1) or (-21/20-1)`
= `"R"/100(1/20) or (-41/20)`
= `"R" = (1/20 xx 100) or (-41/20 xx 100)`
= R = 5 or R = −205
Hence, the rate of increase in the population is 5 p.c.p.a.
RELATED QUESTIONS
Compute the amount and the compound interest in the following by using the formulae when:
Principal = Rs 5000, Rate = 10 paise per rupee per annum, Time = 2 years
Compute the amount and the compound interest in the following by using the formulae when:
Principal = Rs 12800, Rate = \[7\frac{1}{2} %\], Time = 3 years
There is a continuous growth in population of a village at the rate of 5% per annum. If its present population is 9261, what it was 3 years ago?
The annual rate of growth in population of a certain city is 8%. If its present population is 196830, what it was 3 years ago?
The population of a city increases each year by 4% of what it had been at the beginning of each year. If the population in 1999 had been 6760000, find the population of the city in (i) 2001 (ii) 1997
The population of a city increases each year by 4% of what it had been at the beginning of each year. If the population in 1999 had been 6760000, find the population of the city in (i) 2001 (ii) 1997.
.
Jitendra set up a factory by investing Rs 2500000. During the first two successive years his profits were 5% and 10% respectively. If each year the profit was on previous year's capital, compute his total profit.
The value of a machine depreciates at the rate of 10% per annum. What will be its value 2 years hence, if the present value is Rs 100000? Also, find the total depreciation during this period.
Gautam takes a loan of ₹ 16,000 for 2 years at 15% p.a. compound interest. He repays ₹ 9,000 at the end of the first year. How much must he pay at the end of the second year to clear the debt?
Find the amount and the compound interest on ₹ 4,000 in 2 years, if the rate of interest for the first year is 10% and for the second year is 15%.
The value of a car, bought for Rs 4,40,000 depreciates each year by 10% of its value at the beginning of that year. So its value becomes Rs 3,08,000 after three years.
