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?
- (a) 250
- (b) 240 ✓ UPSC's answer
- (c) 230
- (d) 225
Why the answer is (b)
• Let the total number of households be T.
• The percentage of households earning between ₹30,000 and ₹1,00,000 is calculated by subtracting the percentage earning less than ₹30,000 (12%) from the percentage earning less than or equal to ₹1,00,000 (100% - 22% = 78%), resulting in 78% - 12% = 66%.
• Given that 66% of households equals 990, we solve for T: 0.66 * T = 990, which gives T = 1500 households.
• The percentage of households earning between ₹1,00,000 and ₹2,00,000 is the difference between those earning more than ₹1,00,000 (22%) and those earning more than ₹2,00,000 (6%), which is 22% - 6% = 16%.
• Calculating 16% of the total 1500 households: 0.16 * 1500 = 240.
• Therefore, 240 households earn between ₹1,00,000 and ₹2,00,000 per year.
Why the other options are wrong
- (a) 250
- 250 is incorrect because it does not equal 16% of the total 1500 households.
- (c) 230
- 230 is incorrect because it does not equal 16% of the total 1500 households.
- (d) 225
- 225 is incorrect because it does not equal 16% of the total 1500 households.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.