Question

The population of Delhi two years ago was 55000. It increased by $$12\mathrm{\%}$$ in the first year and decreased by $$15\mathrm{\%}$$ in the second year. What was the population of town at the end of 2 years.

Answer 1

Hint: Here, we will find the increment in the population and add it to the given population of Delhi two years ago, we will get the population after one year. Then we will find the decrease in this population and subtract it from the population after one year, we will get the required population of the town at the end of 2 years.

Complete step-by-step answer:
It is given that the population of Delhi two years ago was 55000.
Now, it increased by $$12\mathrm{\%}$$ in the first year. So,
Increase in population $$=12\mathrm{\%}$$ of 55000
$$\Rightarrow$$ Increase in population $$={\displaystyle \frac{12}{100}}\times 55000$$
Multiplying the terms, we get
$$\Rightarrow$$ Increase in population $$=6600$$
Hence, after one year, the total population $$=55000+6600=61,600$$
Now, it is given that the population decreased by $$15\mathrm{\%}$$ in the second year
Decrease in population $$=15\mathrm{\%}$$ of 61600
$$\Rightarrow$$ Decrease in population $$={\displaystyle \frac{15}{100}}\times 61600$$
Multiplying the terms, we get
$$\Rightarrow$$ Decrease in population $$=9240$$
Since, the population has decreased, so we will do subtraction.
Therefore, the population of town at the end of 2 years $$=61600-9240=52,360$$
Hence, the required population of the town at the end of 2 years was 52360.

Note: We are given the increase and decrease in population of the given town in percentages. Now, in order to find the value by which there has been an increase or decrease, we calculate the percentage of increase or decrease on the given value and then, add or subtract the value obtained to the original value. Here, we can make mistakes by calculating the decreased population at the end of two years on the given population before the increase. As it is given that the population has increased after one year so we will take into account the population after an increase, for the calculation of decreased population and not the population before 2 years.