During one year, the population of a town increased by 5% and during the next year, the population decreased by 5%. If the total population is 29925 at the end of the second year, then what was the population size in the beginning of the first year?
30000
To determine the initial population of the town at the beginning of the first year, we need to analyze the changes in population over the two-year period.
- Let the initial population be \(P\).
- During the first year, the population increased by 5%. The population at the end of the first year can be calculated as: \(P_{1} = P + 0.05P = 1.05P\).
- During the second year, the population decreased by 5%. The population at the end of the second year, using the population at the end of the first year, is given by: \(P_{2} = 1.05P - 0.05 \times 1.05P = 1.05P \times (1 - 0.05)\).
- Simplifying, we find: \(P_{2} = 1.05P \times 0.95 = 0.9975P\).
- It is given that the population at the end of the second year is 29925. Therefore, we have the equation: \(0.9975P = 29925\).
- Solving for \(P\): \(P = \frac{29925}{0.9975}\).
- Calculating the value of \(P\) gives: \(P = 30000\).
Therefore, the population at the beginning of the first year was 30,000.
Let's verify the steps:
| Year | Population Change | Calculation | Population |
|---|---|---|---|
| Start of Year 1 | Initial | - | \(30000\) |
| End of Year 1 | 5% Increase | \(30000 \times 1.05 = 31500\) | \(31500\) |
| End of Year 2 | 5% Decrease | \(31500 \times 0.95 = 29925\) | \(29925\) |
Thus, all calculations are consistent, confirming our initial population as 30,000. Therefore, the correct option is 30000.
Similar Questions
If the radius of a circle is increased by 10%, its area will increase by—
Swati's salary is 30% more than Ajay's salary. By what approximate percentage is Ajay's salary less than Swati's salary?
If the price of sugar increases by 25%, determine the percentage by which its consumption be reduced so as not to increase the expenditure on it?
If 3% of (a + b) = 7% of (ab)
and 5 % of (a − b) = 4% of (ab),
then what percentage of b is a?The length of the side of a square (5.0 cm × 5.0 cm) is increased by 1%. By what percentage (%) the area of the square increases?
If 60% of (a − b) = 40% of (a + b), then what percent of a is b?
Manoj's commission is 10% on all sales up to Rs. 10,000 and 5% on all sales exceeding this. He remits Rs. 75,500 to his company after deducting his commission. The total sales will come out to be:
If x and y are two positive numbers and x is 25% greater than y, what is the value of the ratio y/x?
5% of the inhabitants of a village having died of malaria, a panic set in. During this, 20% of the remaining inhabitants left the village. The population is then reduced to 4750. Find the number of original inhabitants?
In a class, 20% of the boys have blue eyes and 10% of the girls have blue eyes. If the ratio of boys to girls in the class is 4:3, then what is the portion of the students in the class having blue eyes?
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:
