Latest Elitmus Aptitude Question SOLUTION: According to the 2001 census,the population growth rate of Lucknow is going to be an increasing AP with first year's rate as 5% and common difference as 5% but simultaneously the m

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(#M40157141) ELITMUS Numerical Ability question Keep an EYE

According to the 2001 census,the population growth rate of Lucknow is going to be an increasing AP with first year's rate as 5% and common difference as 5% but simultaneously the migration,rate is an increasing GP with first term as 1% and common ratio of 2.If the population on 31 december 2000 is 1 million,thn find in which year will Lucknow witness its first fall in population?

Asked In Elitmus Sniper (7 years ago)

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amit  (7 years ago)

population growth rate according to the problem
year 1 = 5%
year 2 = 10%
year 3 = 15%
year 4 = 20%
year 5 = 25%
year 6 = 30%

population decrease due to migration
year 1 = 1%
year 2 = 2%
year 3 = 4%
year 4 = 8%
year 5 = 16%
year 6 = 32%

Thus, the first fall would happen in year 2006

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Aiman Shakeel  (7 years ago)

In sixth year i.e.2006,migration rate(2^5=32%) is more than the population growth rate (30%).
So there will be first population fall in 2006.

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abhijeet bunkar  (7 years ago)

fall in 2006

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rajat  (7 years ago)

acc to my answer the downlfall is occur if migrating people sum is more than increasing population.
total people will be sum in ap and gp.
5% of 1million=5000000. common difference is 5%of 1 million 5000000.
so sn=n/2*(2a+(n-1)d).
sn=n/2*(5000000+(n-1)*5000000);
solving this 2500000n*n.
migration rate is same.
a=1% of million =1000000
sn=a(1-rpower(n))/(1-r);
gn=1000000(1-2power(n))/1-2=1000000*2power(n);
so put n=1,2,3,4,5,6,7,
and check for gn>sn...
but only 8 it decrease gnis greater then sn and 2008 is answer

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