Question : The population of the city was 12,50,000 in the year 2010. It increased at the rate of 2% per annum during the years 2011 and 2012. In the year 2013, it decreased by 1%. Find the population of the city at the end of 2013.
Option 1: 1,28,54,952
Option 2: 13,50,000
Option 3: 13,87,495
Option 4: 12,87,495
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Correct Answer: 12,87,495
Solution : The population of the city in 2010 is 1250000. Then, Population, $P$ = 1250000 Rate of increment, $R$ = 2% We have to find the population at the end of the year 2012, i.e. time, $n$ = 2 years Population after 2 years is given by New Population $= P(1+\frac{R}{100})^n$ $=1250000(1+\frac{2}{100})^2$ $=1250000\times \frac{51}{50}\times \frac{51}{50}$ $=13,00,500$ Again it decreased by 1% $R = –1$% New Population $= P(1-\frac{R}{100})$ $=1300500(1-\frac{1}{100})$ $=1300500\times \frac{99}{100}$ $=12,87,495$ Hence, the correct answer is 12,87,495.
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Question : Two years ago, the population of a small town was 60,000. It increased by 5% in the first year, but due to the pandemic, it decreased by 10% in the second year. What is its present population (after the end of 2 years)?
Option 1: 56,700
Option 2: 56,900
Option 3: 3300
Option 4: 55,700
Question : The population of a city increases compounded by 10% annually. The present population of this city is 1,33,100. What was the population of the city 2 years ago?
Option 1: 1,01,000
Option 2: 1,10,000
Option 3: 1,21,000
Option 4: 1,00,000
Question : The income of a company increases 20% per year. If the income is Rs. 26,64,000 in the year 2012, then its income in the year 2010 was:
Option 1: Rs. 28,55,000
Option 2: Rs. 18,50,000
Option 3: Rs. 28,20,000
Option 4: Rs. 21,20,000
Question : Two years ago, the population of the city was 5,00,000 If the annual birth rate and the annual death rate are 6% and 3%, respectively, what is the present population of the city?
Option 1: 536440
Option 2: 580440
Option 3: 530450
Option 4: 540550
Question : If a number is increased by 25% and the resulting number is decreased by 25%, then the percentage increase or decrease finally is:
Option 1: no change
Option 2: decreased by $6\tfrac{1}{4}$%
Option 3: increased by $6\tfrac{1}{4}$%
Option 4: increased by $6$%
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