Question

A census showed that from 1990 to 2000, a country’s population increased by 25.3%. The country reported its population in 2000 to be 15,264,465. What was the country’s population in 1990?

Answer 1

12,182,334

Explanation:

If some quantity q increases by r%, then the increment will be
`(qr)/(100)`. The new quantity Q (increased) will be

`Q=q+(qr)/(100)=q(1+(r)/(100))`

If we know the final quantity, we can know the original q as

`\displaystyle q=(Q)/(1+(r)/(100) )`

The census showed the rate of increase of the population was r=25.3% and the final population in 2000 was Q=15,264,465. So we can know the population back in 1990 was

`\displaystyle q=(15,264,465)/(1+(25.3)/(100))\approx 12,182,334`