Population Calculation: Past Value
The question asks for the village population two years ago, given the current population and the annual growth rate. This requires reversing the compound growth formula.
Understanding Annual Growth
An annual increase of 8% means that each year, the population is multiplied by a factor of $1 + 0.08 = 1.08$. To find the population two years ago, we need to divide the current population by this factor twice.
Mathematical Approach
Let the population two years ago be $P$. The population after one year was $P \times (1.08)$. The population after two years (the current population) is $P \times (1.08) \times (1.08) = P \times (1.08)^2$. We are given the current population is 58,320.
Therefore, we need to solve the equation:
$ P \times (1.08)^2 = 58,320 $Calculating Past Population
- Calculate the growth factor squared: $(1.08)^2 = 1.1664$.
- Set up the equation to find $P$: $P \times 1.1664 = 58,320$.
- Solve for $P$ by dividing the current population by the squared growth factor: $ P = \frac{58,320}{1.1664} $
- Perform the division: $ P = 50,000 $
The population two years ago was 50,000.
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Important Questions from Percentage
Radha saves 25% of her income. If her expenditure increases by 20% and her income increases by 29%, then her savings increase by;
The income of A is 45% more than the income of B and the income of C is 60% less than the sum of the incomes of A and B. The income of D is 20% more than that of C. If the difference between the incomes of B and D is Rs. 13200, then the income (in Rs.) of C is:
The price of cooking oil increased by 25%. Find by how much percentage a family must reduce its consumption in order to maintain the same budget.
The population of a city increased by 30% in the first year and decreased by 15% in the next year. If the present population is 11,050 then population 2 years ago was:
The income of A is 30% less than the income of B and the income of B is 137.5% more than that of C. If the income of A is Rs. 28500 less than that of B, then the income (in Rs.) of C is:
