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In a small district of Bihar, Population is divided into two categories, SC and OBC category. 60% of total population are under SC category, in which 20% population have monthly earning greater than Rs. 10,000 and in OBC category, 60% population have monthly earning greater than Rs. 10,000. Find what percent of total population have monthly earning less than or equal to 10,000?

In a small district of Bihar, Population is divided into two categories, SC and OBC category. 60% of total population are under SC category, in which 20% population have monthly earning greater than Rs. 10,000 and in OBC category, 60% population have monthly earning greater than Rs. 10,000. Find what percent of total population have monthly earning less than or equal to 10,000? Correct Answer 64%

Given:

60% of total population are under SC category

20% of SC category have monthly income greater than Rs. 10,000

60% of OBC category have monthly income greater than Rs. 10,000

Calculation:                                   

Let the total population of the district be x

SC population = 60% of x = 3x/5

OBC population = 40% of x = 2x/5

Total population in SC category having earning greater than 10,000 = 20% of 3x/5 = 3x/25

Total population in OBC category having earning greater than 10,000 = 60% of 2x/5 = 6x/25

Total population in the District, having earning greater than 10,000 = (3x/25) + (6x/25) = 9x/25

⇒ Total population (SC + OBC), having earning less than or equal to 10,000 = x – (9x/25) = 16x/25

⇒ Required percentage = (16x/25) ÷ x × 100

⇒ (16x × 100)/25x = 64%

∴ 64% of the total population has earning less than or equal to Rs. 10,000

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