In the year 2022, an office had a total of 9,000

Solution

ATQ, Let the number of males and number of females in the office in 2022 be '6x' and '16y', respectively. Total number of employees in 2022 = 6x + 16y = 9000 Divide the above equation with 2, we get, 3x + 8y = 4500 .... (I) Number of males  in 2023 = (7/6) X 6x = '7x' Number of females in 2023 = 1.0625 X 16y = '17y' Total number of employees in 2023 = 7x + 17y = 10000 .... (II) On multiplying equation (I) with 7 and equation (II) with 3, and then subtracting them, we get; 21x + 56y - 21x - 51y = 4500 X 7 - 10000 X 3 Or, 5y = 31500 - 30000 So, y = (1500/5) = 300 By putting the value of 'y' in equation (I) , we get, 3x + 8 X 300 = 4500 Or, 3x = 4500 - 2400 So, x = (2100/3) = 700 Number of males in 2022 = 6x = 6 X 700 = 4,200 Number of females in 2022 = 16y = 16 X 300 = 4,800 Number of males in 2023 = 7x = 7 X 700 = 4,900 Number of females in 2023 = 17y = 17 X 300 = 5,100 For statement I: Difference between the number of males and number of females in 2022 = 4800 - 4200 = 600 So, the data given in statement-I is true. Number of males in 2022 = 6x = 6 X 700 = 4,200 Number of males in 2023 = 7x = 7 X 700 = 4,900 Required average = (4200+4900)/2 = 4,550 So, the data given in statement-II is true. For statement III: Number of females in 2022 = 4,800 Number of females in 2023 = 5,100 Required sum 0.25 X 4800 + 0.3 X 5100 1200 + 1530 =  2,730 So, the data given statement-III is true. Therefore, data given in all three statements are true.