The population of a place increased to 50,000 from 2016 to 2018 at the rate of 6% per annum, and continued the same trend for the next 3 years. If A is the population in 2016 and B is the population in 2020, both are approximated to the next possible integers, then the value of B − A is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 11680.
The population in 2016 was A.
After 2 years at 6% per annum, the population in 2018 = A(1 + 6/100)2 = 50000
⇒ A(1.06)2 = 50000
⇒ 1.1236A = 50000
⇒ A = 50000/1.1236 ≈ 44500 (rounded to the nearest integer)
The population continues to grow at 6% per annum for the next 2 years (from 2018 to 2020).
Population in 2020 (B) = 50000 × (1.06)2 = 50000 × 1.1236 = 56180
Now, B - A = 56180 - 44500 = 11680
Therefore, the value of B - A is 11680.