In an office, the number of men exceeds the number of women by 13. The average weight of all employees (men and women) is 5 kg higher than the average weight of the women. What is the average weight of the men in the office? Statement I: If there were 8 fewer men and 8 more women, the number of men would be 5% less than the number of women. Statement II: If the average weight of each man increased by 4 kg and the average weight of each woman decreased by 5 kg, the overall average weight of all employees would remain the same.

Solution

ATQ, Let the number of women in the office = ‘x’ Then, number of men in the office = (x + 13) Let the average weight of a women in the office = ‘y’ kg Then, average weight of the office = (y + 5) kg Statement I: According to the statement, (x + 13 – 8) = (x + 8) × 0.95 Or, x + 5 = 0.95x + 7.6 Or, x = 2.6 ÷ 0.05 = 52 So, number of women and men in the office is 52 and 65, respectively. So, total weight of the office = (52 + 65) × (y + 5) = (117y + 585) kg Total weight of the women in the office = ‘52y’ kg So, total weight of the men in the office = 117y + 585 – 52y = (65y + 585) kg So, average weight of a men in the office = (65y + 585) ÷ 65 = (y + 9) kg We cannot solve further to obtain the exact value of (y + 9). So, data in statement I alone is not sufficient to answer the question. So, average weight of a boy in the office = (65y + 585) ÷ 65 = (y + 9) kg We cannot solve further to obtain the exact value of (y + 9). So, data in statement I alone is not sufficient to answer the question. Statement II: Let the original average weight a men in the office = ‘z’ kg Then, according to the statement, (x + 13) × (z + 4) + x × (y – 5) = (x + 13) × z + x × y Or, xz + 13z + 4x + 52 + xy – 5x = xz + 13z + xy Or, xz + 13z + 52 + xy – x = xz + 13z + xy Or, xy + 52 – x = xy So, x = 52 So, the number of men and women in the office is 65 and 52, respectively. But with this information alone we cannot determine the average weight of a men in the office. So, data in statement II alone is not sufficient to answer the question. Combining statements I and II: Since, number of women and men in the office is 52 and 65, respectively. We have, 52 × y + 65 × (y + 9) = 52 × (y – 5) + 65 × (y + 9 + 4) Or, 52y + 65y + 585 = 52y – 260 + 65y + 845 Or, 117y + 585 = 117y + 585 This equation cannot be solved any further, So, data in statements I and II together are not sufficient to answer the question.