The rabbit population in community A increases at 25% per year while that in community B increases at 50% per year. If the present populations of A and B are equal, what will be the ratio of the number of rabbits in community B to that in community A after 2 years ?
1.44
1.72
1.90
1.25
Answer is Right!
Answer is Wrong!
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UPSC CISF-AC-EXE – 2017
Population growth in community A is 25% per year. After ‘n’ years, the population will be P * (1 + 0.25)^n.
Population growth in community B is 50% per year. After ‘n’ years, the population will be P * (1 + 0.50)^n.
We need to find the ratio of the number of rabbits in community B to that in community A after 2 years (n=2).
Population of B after 2 years = P_B(2) = P * (1 + 0.50)² = P * (1.50)² = P * 2.25.
The ratio of the number of rabbits in community B to that in community A after 2 years is P_B(2) / P_A(2).
Ratio = (P * 2.25) / (P * 1.5625) = 2.25 / 1.5625.
To calculate 2.25 / 1.5625, we can write it as 22500 / 15625.
Divide both by 25: 900 / 625.
Divide both by 25 again: 36 / 25.
36 / 25 = 1.44.
The ratio is 1.44.