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Question 13

Suppose hospital A admitted 21 less Covid infected patients than hospital B, and all eventually recovered. The sum of recovery days for patients in hospitals A and B were 200 and 152, respectively. If the average recovery days for patients admitted in hospital A was 3 more than the average in hospital B then the number admitted in hospital A was


Correct Answer: 35

Solution

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Let the number of Covid patients in Hospitals A and B be x and x+21, respectively. Then, it has been given that:

$$\dfrac{200}{x}-\dfrac{152}{x+21}=3$$

$$\dfrac{\left(200x+4200-152x\right)}{x\left(x+21\right)}=3$$

$$\dfrac{\left(48x+4200\right)}{x\left(x+21\right)}=3$$

$$16x+1400=x\left(x+21\right)$$

$$x^2+5x-1400=0$$

(x+40)(x-35)=0

Hence, x=35.

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