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Question :

Directions : Study the data carefully and answer the following questions:

Below data is given regarding the number of patients who tested positive for COVID-19 in four hospitals (A, B, C and D) in four weeks of a month. Total number of patients who tested positive for COVID-19 in all four hospitals together in all the four weeks of the month together is 50 thousands.

In Hospital A: The ratio of number of patients who tested positive for COVID-19 in 1st, 2nd and 3rd week is 3: 2: 4 respectively. The number of patients who tested positive for COVID-19 in 4th week is equal to the number of patients who tested positive for COVID-19 in 2nd week of hospital B.

In Hospital B: In week 3rd, the number of patients who tested positive for COVID-19 is 500 less than that in hospital D. The number of patients who tested positive for COVID-19 in 1st week is 1000 more than the number of patients who tested positive for COVID-19 in 2nd week. The number of patients who tested positive for COVID-19 in 4th week is half of the number of patients who tested positive for COVID-19 in 2nd week in hospital A. The number of patients who tested positive for COVID-19 in all the four weeks together is 1500 more than the total number of patients who tested positive for COVID-19 in 1st week in hospital C.

In Hospital C: The number of patients who tested positive for COVID-19 in 2nd week is thrice of the number of patients who tested positive for COVID-19 in 1st week in hospital D. The number of patients who tested positive for COVID-19 in 3rd week is 25% of number of patients who tested positive for COVID-19 in 2nd week. The number of patients who tested positive for COVID-19 in 4th week is equal to the number of patients who tested positive for COVID-19 in 3rd week in hospital B. The number of patients who tested positive for COVID-19 in 1st week is 87.5% more than the number of patients who tested positive for COVID-19 in 3rd week in hospital A. The number of patients who tested positive for COVID-19 in all the four weeks together is 36% of total number of patients who tested positive for COVID-19 in all the four hospitals in all the four weeks together.

In Hospital D: The ratio of number of patients who tested positive for COVID-19 in 1st, 2nd, 3rd and 4th week is 4: 8: 7: 5 respectively.

The number of patients who tested positive for COVID-19 in 2nd and 3rd weeks together in hospital C is what percentage more or less than the number of patients who tested positive for COVID-19 in 1st and 4th weeks together in hospital D?

1. 45.45%

2. 66.66%

3. 33.33%

4. 75.45%

5. 29.49%

Correct Answer : 2
Solution :

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 1Week 2Week 3Week 4Total
Hospital A300020004000200011000
Hospital B30002000300010009000
Hospital C750060001500300018000
Hospital D200040003500250012000
Total155001400012000850050000

The number of patients who tested positive for COVID-19 in 2nd and 3rd weeks together in hospital C = 6000 + 1500 = 7500

The number of patients who tested positive for COVID-19 in 1st and 4th weeks together in hospital D = 2000 + 2500 = 4500

So, required % = (7500 - 4500)/4500 * 100 = 66.66%

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