Multiple choice

10 skilled men and 5 skilled women can complete a work in 4 days, while 8 skilled men and 10 skilled women can complete the same work in 3 days. The efficiency of unskilled men is 40% less than the efficiency of skilled men and the efficiency of unskilled women is 50% less than the efficiency of skilled women. Quantity I: Time taken to complete the whole work by 4 unskilled men and 1 skilled woman. Quantity II: Time taken to complete the whole work by 5 unskilled women and 1 skilled man.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or No relation
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A Correct answer
Explanation

Let Sm and Sw be efficiencies of skilled men and women. Unskilled men = 0.6 Sm, unskilled women = 0.5 Sw. From the equations (10Sm+5Sw)*4 = (8Sm+10Sw)*3, we find 40Sm+20Sw = 24Sm+30Sw, so 16Sm = 10Sw or Sw = 1.6Sm. Total work = 60Sm. Quantity I: 4(0.6Sm) + 1(1.6Sm) = 4Sm, time = 60/4 = 15. Quantity II: 5(0.5*1.6Sm) + 1(Sm) = 5Sm, time = 60/5 = 12. Since 15 > 12, I > II.

AI explanation

From the first condition, 40 men plus 20 women equals 1 by 4 of the work per day, and from the second, 24 men plus 30 women equals 1 by 3 of the work per day. Solving these two equations, one skilled man does 1 by 120 of the work per day and one skilled woman does 1 by 120 of the work per day. Unskilled men do 60 percent of that, which is 1 by 200, and unskilled women do 50 percent, which is 1 by 240. For Quantity I, 4 unskilled men and 1 skilled woman do 4 by 200 plus 1 by 120, equaling 11 by 600, taking 54.54 days. For Quantity II, 5 unskilled women and 1 skilled man do 5 by 240 plus 1 by 120, equaling 7 by 240, taking 34.28 days. Comparing the two, 54.54 days is greater than 34.28 days.

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