Solution:Given, average number of patients in hospitals R and S together = 460
Total number of patients in hospital R and S together = 460 × 2 = 920
Let the total number of patients in hospital R be ‘t’
Therefore, total number of patients in hospital S = 920 - t
Given, average number of patients in hospitals S and T together = 420
Total number of patients in hospital S and T together = 420 × 2 = 840
Let the total number of patients in hospital T = 840 - (920 - t)
= t - 80
Ratio of the total number of patients in hospital S to that of hospital T = 2:1
According to the question:
=> (920 - t) / (t - 80) = 2/1
=> 920 - t = 2t - 160
=> 3t = 1080
=> t = 360
Hence, total number of patients in hospital R = 360
Ratio of the number of male patients to female patients in hospital R = 5:4
Therefore, number of male patients in hospital R
= (5/9) × 360 = 200
Number of female patients in hospital R = 360 - 200 = 160
Total number of patients in hospital S = 920 - 360 = 560
Let the number of female patients in hospital S be 5p
Therefore, number of male patients in hospital S
= (3/5) × 5p = 3p (40% less than female patients)
According to the question:
=> 5p + 3p = 560
=> 8p = 560
=> p = 70
Hence, number of female patients in hospital S = 5p = 5 × 70 = 350
And number of male patients in hospital S = 560 - 350 = 210
Total number of patients in hospital T = 360 - 80 = 280
Ratio of the number of male patients to female patients in hospital T = 3:2
Therefore, number of male patients in hospital T
= (3/5) × 280 = 168
And number of female patients in hospital T = 280 - 168 = 112
Hospital | Total patients | Male patients | Female patients
R | 360 | 200 | 160
S | 560 | 210 | 350
T | 280 | 168 | 112
Total female patients in hospitals R and S together
= 160 + 350 = 510
Total number of patients in hospital T = 280
Hence, required difference = 510 - 280 = 230 more