# How do I solve this problem on successive percentages?

Question: " The population of a city in 2017 increased by 12.5 % from 2016 and in 2018 it decreased by 8 % with respect to previous year and in 2019 it again increased by 15 % with respect to previous year. If in 2019, the population of the city is 1190250,then what was the population of city in 2016?"

My doubt is exactly whether the increased population is after 2019 or in 2019. Eitherways how do I calculate the value from there. A detailed guidance into the same will be most welcome. Infact the calculation behind the process will be very helpful for me. What is the thinking process behind successive percentage? Some amount of help will be most welcome.

• If the population increases by $12.5\%$ it was multiplied by $1.125$. The same applies to each other step. That gives you the multiplier for the three years. The question does not say whether the given $2019$ population is after the increase but I would assume so. You should state that assumption in your answer. There is no mention of salary in the problem. Jun 9, 2022 at 4:59
• Replace each occurrence of "in/from ?" with "on/from census day in ?". That might address your confusion here where it is treating population vs time as a discrete process rather than years being continuous. Jun 9, 2022 at 5:24

I think this is a classic type of exercise, to stress the fact that applying percentages to a number in different orders leads to different results. The way I would approach this is by writing one equation per statement, using the population in various years as variables. For example, supposing the population at year $$y$$ is called $$P_y$$, from the data in the text: $$P_{17} = 1.125 P_{16}$$ $$P_{18} = 0.92 P_{17}$$ $$P_{19} = \ldots P_{18}$$ and I'll leave the coefficient in the last equation to you. Then, since the text gives you the value of $$P_{19}$$, you can work your way bak one year at a time to find $$P_{16}$$. My interpretation is that $$1190250$$ is the population at the end of $$2019$$.