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

Correct Option (B)

The total percentage of households in the city is considered as 100%.

Given data:

• Households earning less than Rs. 30,000 per year: 12%.
• Households earning more than Rs. 1,00,000 per year: 22%.
• Households earning between Rs. 30,000 and Rs. 1,00,000 per year: 990 households.

The percentage of households earning between Rs. 30,000 and Rs. 1,00,000 can be determined by subtracting the other known percentages from the total:

Percentage (Rs. 30,000 - Rs. 1,00,000) = 100% - (Percentage < Rs. 30,000 + Percentage > Rs. 1,00,000)

= 100% - (12% + 22%)

= 100% - 34% = 66%.

Since 66% of the total households corresponds to 990 households, the total number of households in the city is calculated as:

Total Households = 990 × $\frac{100}{66}$ = 1500 households.

To find the number of households earning between Rs. 1,00,000 and Rs. 2,00,000, we use the given percentages:

• Households earning more than Rs. 1,00,000: 22% of total households.
• Households earning more than Rs. 2,00,000: 6% of total households.

The percentage of households earning specifically between Rs. 1,00,000 and Rs. 2,00,000 is the difference between these two categories:

Percentage (Rs. 1,00,000 - Rs. 2,00,000) = Percentage > Rs. 1,00,000 - Percentage > Rs. 2,00,000

= 22% - 6% = 16%.

Finally, the number of households in this income bracket is 16% of the total households:

Number of Households = 16% of 1500

= $\frac{16}{100}$ × 1500 = 240 households.

Incorrect Options:

Options A (250), C (230), and D (225) are incorrect. These values would arise from errors in calculating the total number of households, misinterpreting the income brackets, or performing incorrect arithmetic operations based on the provided percentages.