Question

The population of a city increases by 10% in 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. 1,00,000
• B. 1,11,000
• C. 90,000
• D. 1,00,210

Answer 1

The correct option is B

1,11,000

Let the population in the year 1980 be x
$\therefore$ The population in the year 1985 = x + (10% of x)
$=x+\frac{10}{100}\times x=\frac{11x}{10}$
$\therefore$ 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}+\frac{10}{100}\times \frac{11x}{10}$

$⟹$$\frac{11x}{10}+\frac{11x}{100}$
$⟹$$\frac{110x+11x}{100}$
$⟹$$\frac{121x}{100}$
According to the problem,

Population of the city in the year 1990 =1,34,310
$⟹$$\frac{121x}{100}$ = 1,34,310
$or,x=1,34,310\times \frac{100}{121}=1,11,000$