Question

In one year, the population of a village increased by 10% and on the next year, it decreased by 10%. If the end of the 2nd year, the population was 7920, what was it in the beginning?

• A. 8500
• B. 8000
• C. 8100
• D. 840

Answer 1

Answer: (B)

8000

Let the initial population be x

In $1^{st}$ year population increased by = 10 %

10 % increase is population $=\frac{10}{100x}=0.1x$

After $1^{st}$ year population $=x+0.1x=1.1x$

After $2^{nd}$ 10% decrease, $90\%$ of $1^{st}$ year

population = $\left(\frac{90}{100}\right)\times 1.1x$

At the end of $2^{nd}$ year population = $7920$

Hence $0.99x=7920$

$x=7920÷0.99$

$x=792000÷99$

$x=8000$

$\therefore$ The population at the beginning was $8000$

option B is correct