CAT 2021 Slot 1 QA Question 10: 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

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

Accepted Answer

Let the number of patients admitted in hospital A be $x$. Then hospital B admitted $x + 21$ patients.
Average recovery days in A is 3 more than that in B.
$\dfrac{200}{x} = \dfrac{152}{x+21} + 3$
$200(x+21) = 152x + 3x(x+21)$
$3x^2 + 15x - 4200 = 0$
$x^2 + 5x - 1400 = 0$
$(x-35)(x+40) = 0$
Since $x$