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    Question

    In the year 2022, an office had a total of 9,000 employees, including both males and females. In the following year, the number of male employees increased by (50/3)% and the number of female employees grew by 6.25%, leading to a total workforce of 10,000 employees. Which of the following statements is/are accurate?

    I. The difference between the number of male and female employees in the office in 2022 is 600.

    II. The average number of male employees in the office across 2022 and 2023 is 4,550.

    III. The sum of 25% of the number of female employees in 2022 and 30% of the number of female employees in 2023 is 2,730.

    A Only I Correct Answer Incorrect Answer
    B Only II Correct Answer Incorrect Answer
    C Only I and III Correct Answer Incorrect Answer
    D Only II and I Correct Answer Incorrect Answer
    E All of I, II and III are true Correct Answer Incorrect Answer

    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.

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