Question

The population of a city increases by 10% every 5 years. If the population of the city in the year 1990 is 1,34,310. What was the population in the year 1980?

• A. 1,11,000
• B. 1,34,500
• C. 1,56,500
• D. 1,21,000

Answer 1

The correct option is A

1,11,000

Let the population in the year 1980 be
$x.$

$\therefore$ The population in the year 1985
$=x+10\%ofx$
$=x+\frac{10}{100}\times x=\frac{11x}{10}$

$\therefore$ The population in the year 1990
$=\frac{11x}{10}+10\%of\frac{11x}{10}$
$\Rightarrow \frac{11x}{10}+\frac{10}{100}of\frac{11x}{10}$

$\Rightarrow \frac{11x}{10}+\frac{10}{100}\times \frac{11x}{10}$

$\Rightarrow \frac{11x}{10}+\frac{11x}{100}$

$=\frac{110x+11x}{100}$

$=\frac{121x}{100}$

According to the problem,

Population of the city in the year 1990 =1,34,310

$\Rightarrow \frac{121x}{100}=1,34,310$

$or,x=1,34,310\times \frac{100}{121}=1,11,000$