Question

The population of a city is $7.26$ lakh today. If the population has been increasing at the rate of $10\%$ per year, then two year ago, the population would have been

• A. $6$ lakh
• B. $5.5$ lakh
• C. $5$ lakh
• D. $4.5$ lakh

Answer 1

Answer: (A)

$6$ lakh

The population at present $=P=7.26$ lakh.

Time $=2$ yrs $=T$. Rate $=10\%$ p.a.

Now, Final population $=$ (original population)$\times {(1+\frac{Rate}{100})}^{time}.$

Here we are to find out the population two years back.

Let it be $x$.

So, the population $2$ yrs. after $=$ $=x{(1+\frac{10}{100})}^2=7.26$

$\Rightarrow x{\left(\frac{11}{10}\right)}^2=7.26$

$\Rightarrow x=7.26\times \frac{10}{11}\times \frac{10}{11}$ lakh

$\Rightarrow x=6$ lakh

$\therefore$ the population was $6$ lakh $2$ years back.

Ans- Option A.