Question

The population of a variety of tiny bush in an experimental field increased by $10\%$ in the first year, increased by $8\%$ in the second year but decreased by $10\%$ in the third. If the present number of bushes in the experimental field is $26730$, then the number of bushes in the beginning was

• A. $25000$
• B. $27000$
• C. $28000$
• D. $24600$

Answer 1

The correct option is A $25000$

Let the number of bushes $=x$ at the onset.

In the first year, the number was increased by $10\%$.

$\therefore$ the number in the first year $=$ $x+x\times \frac{10}{100}=\frac{11x}{10}.$

In the second year this number was increased by $8\%$.

$\therefore$ the number in the second year $=$ $\frac{11x}{10}+\frac{11x}{10}\times \frac{8}{100}=\frac{297x}{250}.$

In the third year this number was decreased by $10\%$.

$\therefore$ the number in the second year $=$ $\frac{297x}{250}-\frac{297x}{250}\times \frac{10}{100}=\frac{2673x}{2500}.$

$\therefore$ By the given condition,

$\frac{2673x}{2500}=26730$

$\Rightarrow x=26730\times \frac{2500}{2673}=25000$

So, the number of the bushes in the beginning was $25000$.

Ans- Option A.