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\(\frac{{11}}{{16}}\) of the residents of a housing society own cars and \(\frac{{20}}{{33}}\) of the car owners have purchased covered parking space. If 130 of the residents parked in the open, how many residents we there in the society?

\(\frac{{11}}{{16}}\) of the residents of a housing society own cars and \(\frac{{20}}{{33}}\) of the car owners have purchased covered parking space. If 130 of the residents parked in the open, how many residents we there in the society? Correct Answer 480

Given,

Number of residents of a housing society own cars is = 11/16 of total residents

Number of residents of car owners have purchased covered parking space = 20/33 of the car owners

Number of residents who parked their car in open = 130

Concept:

If any fraction decreases by a/b, then,

Remaining value = (1 – a/b) × Actual value

Calculation:

Let the total number of residents of a housing society be x

Number of residents who own cars = x × 11/16 = 11x/16

⇒ Number of residents who have covered parking space = (11x/16) × (20/33) = 5x/12

⇒ Number of residents who park their car in open = 11x/16 – 5x/12 = 13x/48

According to the question

13x/48 = 130

x = 130 × (48/13)

x = 480

∴ Number of resident in the society is 480

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