QUESTION

CSAT

Medium

Maths

Prelims 2017

In a city, 12% of households earn less than Rs. 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?

Select an option to attempt

Explanation

Given Data:

  • 12% of households earn less than Rs. 30,000.
  • 6% of households earn more than Rs. 2,00,000.
  • 22% of households earn more than Rs. 1,00,000.
  • 990 households earn between Rs. 30,000 and Rs. 1,00,000.

Let the total number of households be X.

Step 1: Use the total percentage of households

  • 12% of X = 0.12X0.12X (households earning less than Rs. 30,000)
  • 990 households (households earning between Rs. 30,000 and Rs. 1,00,000)
  • Let y be the number of households earning between Rs. 1,00,000 and Rs. 2,00,000
  • 6% of X = 0.06X0.06X (households earning more than Rs. 2,00,000)

Step 2: Use the 22% of households earning more than Rs. 1,00,000

  • 22% of X = 0.22X0.22X (households earning more than Rs. 1,00,000)
  • y+0.06X=0.22Xy + 0.06X = 0.22X
  • y=0.22X0.06X=0.16Xy = 0.22X - 0.06X = 0.16X

Step 3: Use the total number of households

  • 0.12X+990+0.16X+0.06X=X0.12X + 990 + 0.16X + 0.06X = X
  • 0.34X+990=X0.34X + 990 = X
  • 990=X0.34X990 = X - 0.34X
  • 990=0.66X990 = 0.66X
  • X=990/0.66=1500X = 990 / 0.66 = 1500

Step 4: Calculate the number of households earning between Rs. 1,00,000 and Rs. 2,00,000

  • y=0.161500=240y = 0.16 * 1500 = 240

Final Answer: The number of households earning between Rs. 1,00,000 and Rs. 2,00,000 is 240. Answer: B. 240

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