Multiple choice

30 men, working 4 hrs a day can do a piece of work in 10 days. Find the number of days in which 45 men working 8 hrs a day can do twice the work. Assume that 2 men of the first group do as much work in 2 hrs as 4 men of the second group do in 1 hr.

  1. 8(2/3) days

  2. 7(2/3) days

  3. 6(2/3) days

  4. 5(2/3) days

  5. 4(2/3) days
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C Correct answer
Explanation

Using the formula (M1*D1*H1)/W1 = (M2*D2*H2)/W2. The efficiency condition implies 2 men * 2 hrs = 4 men * 1 hr, meaning they have equal efficiency. Thus, (30*10*4)/1 = (45*D2*8)/2. Solving for D2: 1200/1 = 360*D2/2, so 1200 = 180*D2, D2 = 1200/180 = 6.66 or 6(2/3) days.

AI explanation

Let the efficiency of a second group man be 1 unit per hour; the condition states 2 men of the first group do as much work as 4 of the second, so a first group man's efficiency is 2 units per hour. The total work is 30 men times 4 hours times 10 days times 2 units, equaling 2400 units. The second group must do twice this work, which is 4800 units. The second group's daily work is 45 men times 8 hours times 1 unit, equaling 360 units per day. Dividing 4800 units by 360 units per day gives 6 and 2/3 days.

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