Suppose that the people in a certain city are catching cold. It is observed that after one week, 40% of the people who were sick are still sick. Of the people who were well, 30% are sick after one week. If, at some particular time, 20% of the people are ill, find the proportion of people who are sick after two weeks

the proportion of people who are sick after two weeks is 33.2%

Step-by-step explanation:

Given the data in the question;

Let there be 100 people in the city;

20% of them are sick( 20/100 × 100) = 20 people

so 80% are fine = ( 100 - 20 ) = 80

after one week, 40% of the people who were sick are still sick

40/100 × 20 = 8%

of the 80% of people who were well, 30% got sick after one week

30/100 × 80 = 24%

so after one week. 8% + 24% = 32% of the people were sick,

hence 68% are fine.

now, after second week 40% of sick and 30% of not sick people previously will be sick

∴ Total people who are sick after two weeks    

⇒ 40/100 × 32 + 30/100 × 68

= 12.8 + 20.4

= 33.2

Therefore, the proportion of people who are sick after two weeks is 33.2%