Total number of patients who tested positive for COVID-19 in all the four hospitals in all the four weeks of a month is 50 thousands.
In Hospital A:
The number of patients who tested positive for COVID-19 in 1st week = 3x
The number of patients who tested positive for COVID-19 in 2nd week = 2x
The number of patients who tested positive for COVID-19 in 3rd week = 4x
The number of patients who tested positive for COVID-19 in 4th week = k
In Hospital B:
The number of patients who tested positive for COVID-19 in 1st week = (k + 1000)
The number of patients who tested positive for COVID-19 in 2nd week = k
The number of patients who tested positive for COVID-19 in 3rd week = (7y - 500)
The number of patients who tested positive for COVID-19 in 4th week = x
Total number of patients who tested positive for COVID-19 in all four weeks together = (7.5x + 1500)
=> (k + 1000) + k + (7y - 500) + x = (7.5x + 1500)
=> 2k - 6.5x + 7y = 1000 ---(1)
In Hospital C:
The number of patients who tested positive for COVID-19 in 1st week = 187.5% of 4x = 7.5x
The number of patients who tested positive for COVID-19 in 2nd week =3 * 4y = 12y
The number of patients who tested positive for COVID-19 in 3rd week = 25% of 12y = 3y
The number of patients who tested positive for COVID-19 in 4th week = (7y - 500)
Total number of patients who tested positive for COVID-19 in all the four weeks together= 36% of 50000 = 18000
=> 7.5x + 12y + 3y + (7y - 500) = 18000
=> 7.5x + 22y = 18500 ---(2)
In Hospital D:
The number of patients who tested positive for COVID-19 in 1st week = 4y
The number of patients who tested positive for COVID-19 in 2nd week = 8y
The number of patients who tested positive for COVID-19 in 3rd week = 7y
The number of patients who tested positive for COVID-19 in 4th week = 5y
Total number of patients who tested positive for COVID-19 in all the four hospitals in all the four weeks together = 17.5x + 3k + 53y = 50000 ---(3)
Solving above three equations, we get
k = 2000, x = 1000 and y = 500
Tabulating the above data, we get
| Week 1 | Week 2 | Week 3 | Week 4 | Total |
Hospital A | 3000 | 2000 | 4000 | 2000 | 11000 |
Hospital B | 3000 | 2000 | 3000 | 1000 | 9000 |
Hospital C | 7500 | 6000 | 1500 | 3000 | 18000 |
Hospital D | 2000 | 4000 | 3500 | 2500 | 12000 |
Total | 15500 | 14000 | 12000 | 8500 | 50000 |
Required % = 14000/50000 * 100 = 28%