Delhi city population Ist year `15%` increase, Iind year `20%` decrease and IIIrd year `10%` increase. If present population is `101200` then find 3 year before population ?

Options

A. `200000`
B. `400000`
C. `100000`
D. `600000`

Answer

To find the population three years before given the changes over the years, we can set up the problem step by step.

### Step 1: Define the variables
Let the population three years ago be \( X \).

### Step 2: Apply the first year's increase
In the first year, the population increases by 15%. Therefore, the population after the first year can be calculated as:
\[ \text{Population after 1st year} = X + 0.15X = 1.15X \]

### Step 3: Apply the second year's decrease
In the second year, the population decreases by 20%. The population after the second year can be calculated as:
\[ \text{Population after 2nd year} = 1.15X - 0.20(1.15X) = 1.15X \times 0.80 = 0.92X \]

### Step 4: Apply the third year's increase
In the third year, the population increases by 10%. The population after the third year can be calculated as:
\[ \text{Population after 3rd year} = 0.92X + 0.10(0.92X) = 0.92X \times 1.10 = 1.012X \]

### Step 5: Set the equation equal to the present population
According to the problem, the present population is 101200. Therefore, we can set up the equation:
\[ 1.012X = 101200 \]

### Step 6: Solve for \( X \)
To find \( X \), we divide both sides of the equation by 1.012:
\[ X = \frac{101200}{1.012} \approx 100200 \]

Thus, the population three years ago was approximately **100200**.

### Summary of the Steps
1. Define the variable for the population three years ago.
2. Calculate the population after the first year with a 15% increase.
3. Calculate the population after the second year with a 20% decrease.
4. Calculate the population after the third year with a 10% increase.
5. Set the final population equal to the present population and solve for \( X \).