cat 2021 Question 16

Question

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

Accepted Answer

Let the number of Covid patients in Hospitals A and B be $x$ and $x+21$ respectively.

Given that:

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

$\frac{200x + 4200 - 152x}{x(x+21)} = 3$

$\frac{48x + 4200}{x(x+21)} = 3$

$16x + 1400 = x(x + 21)$

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

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

Hence, $x = 35$.

Question 16.

Question Explanation