Question

109. If the town's population was 62,000 at the end of year 5, and the population grew at the same annual rate as the number of eating establishments between the end of year 1 and the end of year 5, what was the town's population at the end of year 1?
A. 49,809
B. 51,435
C. 53,230
D. 54,330
E. 56,730

why the answer is A , and give the process

Answer 1

The eating establishments were as follows for 5 years

(As per the problem in the book) Year 1 = 143; Year 2 = 149; Year 3 = 162; Year 4 = 171; Year 5 = 178

The year by year % increase 4.19 % in year 2, 8.7% in year 3 5.55 % in year 4 and 4.09 % in year 5

Now we back calculate i.e Year 5 end = 62,000

year 4 = 62,000 / 1.0409 = 59,615

year 3 = 59,615/ 1.055 = 56,507

year 2 = 56,507/ 1.087= 51,984

year 1 = 51,984/1.0419 = 49,809

Thats why the answer is (A) 49,809