Question

The population of a city increases by $10\%$ in every 5 year. If the population of the city in the year 1990 is 134310. What was the population in the year 1980?

• A. 111000
• B. 134500
• C. 156500
• D. None of these

Answer 1

The correct option is A 111000

Let the population in the year 1980 be x
$\therefore$ The population in the year 1985 = $x+10\%$ of x
$=x+\frac{x}{10}=\frac{11x}{10}$
$\therefore$ The population in the year 1990 = $\frac{11x}{10}+10\%of\frac{11x}{10}$
= $\frac{11x}{10}+\frac{10}{100}of\frac{11x}{10}$
= $\frac{11x}{10}\left(\frac{110}{100}\right)$
= $\frac{121x}{100}$
$\therefore$ By the problem,
= $\frac{121x}{100}=134210$
$or,x=134310\times \frac{100}{121}=111000$