tulikas024
In city X, the ratio of the number of people who were tested Covid positive to the number of the people who were tested Covid not positive is 70:30. However, 80 percent of the people who did not show Covid symptoms, were tested Covid positive and 60 percent of the people who showed Covid symptoms, did not test Covid positive. Of the people who did not test Covid positive, what was the approximate percent of the people who showed Covid symptoms?
(a) 15%
(b) 45%
(c) 50%
(d) 65%
(e) 70%
We can use a 2*2 matrix to solve the question.
Let's assume that the number of people in city X = 100
- Number of people who were tested positive = \(\frac{70}{100} * 100 = 70\)
- Number of people who were not tested positive = \(\frac{30}{100} * 100 = 30\)
- Number of people who did not show symptom = x
80 percent of the people who did not show Covid symptoms, were tested Covid positive = 80% of x = 0.8x
- Number of people who showed symptom = 100-x
60 percent of the people who showed Covid symptoms, did not test Covid positive = 60% of x
We can equate the number of people who showed symptoms and were actually tested positive ⇒
\(\frac{40}{100}(100-x) = 70-0.8x \)
\(x= \frac{150}{2}\)
Number of people who showed covid symptoms but were not tested positive = 60% of (100 - x)
= \(\frac{60}{100} * (100 - \frac{150}{2}) = 15\)
Required percentage = \(\frac{15}{30} * 100 = 50%\)
Option C
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