In a city, 12% of households earn less than ₹30,000 per year, 6% households earn more than ₹2,00,000 per year, 22% households earn more than ₹1,00,000 per year and 990 households earn between ₹30,000 and ₹1,00,000 per year. How many households earn between ₹1,00,000 and  ₹2,00,000 per year?

The correct answer is 240.

Step-by-step Explanation:

Step 1: Understand the given income distribution percentages

Let the total number of households in the city be $N$.

From the question, we have the following data about the household earnings:

1. Percentage of households earning less than ₹30,000 per year = 12%

2. Percentage of households earning more than ₹2,00,000 per year = 6%

3. Percentage of households earning more than ₹1,00,000 per year = 22%

Step 2: Find the percentage of households in different income brackets

First, let's determine the percentage of households earning between ₹1,00,000 and ₹2,00,000 per year:

Households earning more than ₹1,00,000 include those earning between ₹1,00,000 and ₹2,00,000, as well as those earning more than ₹2,00,000.

Percentage earning between ₹1,00,000 and ₹2,00,000 = (Percentage earning > ₹1,00,000) - (Percentage earning > ₹2,00,000)

$=22\%-6\%=16\%$

Next, let's find the percentage of households earning between ₹30,000 and ₹1,00,000 per year:

The total percentage of all households is 100%.

Households earn between ₹30,000 and ₹1,00,000 if they do not fall under "less than ₹30,000" or "more than ₹1,00,000".

Percentage earning between ₹30,000 and ₹1,00,000 = 100% - (Percentage earning < ₹30,000) - (Percentage earning > ₹1,00,000)

$=100\%-12\%-22\%=66\%$

Step 3: Calculate the total number of households

We are given that 990 households earn between ₹30,000 and ₹1,00,000 per year.

Since 66% of the total households ($N$) corresponds to 990 households:

$66\%\text{ of }N=990$

$\frac{66}{100}\times N=990$

$N=\frac{990\times 100}{66}$

$N=15\times 100=1500$

So, the total number of households in the city is 1,500.

Step 4: Calculate the number of households earning between ₹1,00,000 and ₹2,00,000 per year

We found in Step 2 that 16% of total households earn between ₹1,00,000 and ₹2,00,000 per year.

Number of households = 16% of 1500

$=\frac{16}{100}\times 1500$

$=16\times 15=240$

Thus, 240 households earn between ₹1,00,000 and ₹2,00,000 per year.