Time and Work Questions

Multiple choice
  1. $20$ days
  2. $30$ days
  3. $40$ days
  4. $50$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given 1/A + 1/B = 1/10 and 1/B + 1/C = 1/20. Also 4/A + 6/B + 22/C = 1. Substituting 1/A = 1/10 - 1/B, we get 4(1/10 - 1/B) + 6/B + 22/C = 1, which simplifies to 2/B + 22/C = 0.6. Using 1/B = 1/20 - 1/C, we get 2(1/20 - 1/C) + 22/C = 0.6, so 20/C = 0.5, C = 40.

Multiple choice
  1. $23$ days
  2. $37$ days
  3. $37 \dfrac { 1 } { 2 }$ days
  4. $40$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A does 4/5 in 20 days, so A's rate is (4/5)/20 = 1/25 per day. Remaining work = 1/5. A and B finish 1/5 in 3 days, so their combined rate is (1/5)/3 = 1/15. B's rate = Combined - A = 1/15 - 1/25 = (5-3)/75 = 2/75. B takes 75/2 = 37.5 days.

Multiple choice
  1. $120$ men
  2. $170$ men
  3. $180$ men
  4. $150$ men
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The work formula is (M1*D1)/W1 = (M2*D2)/W2. Initially, 90 men did 2 km in 20 days. Remaining work is 4 km in 15 days. (90*20)/2 = (M2*15)/4. Solving gives M2 = 240. Since 90 men are already there, 150 more are needed.

Multiple choice
  1. $40$
  2. $45$
  3. $50$
  4. $52$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Kamlesh does 75% in 27 days, so his rate is 75/27 = 25/9 percent per day. Together they do 25% in 5 days, so their combined rate is 25/5 = 5 percent per day. Lucifer's rate = 5 - 25/9 = 20/9 percent per day. Time for 100% = 100 / (20/9) = 45 days.

Multiple choice
  1. $20$ days
  2. $30$ days
  3. $50$ days
  4. $40$ days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let M and W be daily work of a man and woman. (6M + 6W) * 24 = 1; (8M + 12W) * 15 = 1. Solving these: 144M + 144W = 120M + 180W => 24M = 36W => M = 1.5W. Substituting, (6*1.5W + 6W) * 24 = 1 => 15W * 24 = 1 => 360W = 1. So 1 woman does 1/360 work/day. 4M + 6W = 4(1.5W) + 6W = 12W. Time = 1 / (12 * (1/360)) = 360/12 = 30 days.

Multiple choice
  1. $10.0$
  2. $12.0$
  3. $15.0$
  4. $18.0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the daily work rates of A and B be a and b, respectively. We have the system of equations a + b = 1/5 and 2a + b/2 = 1/4. Solving this system gives a = 1/10, meaning A alone can complete the work in 10 days.

Multiple choice
  1. $18$
  2. $13$
  3. $22$
  4. $25$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work done = 448m in 27 days by 56 men. Rate = 448 / (56 * 27) = 8/27 m per man-day. Remaining work = 1000 - 448 = 552m. Remaining time = 50 - 27 = 23 days. Required men = 552 / (23 * 8/27) = 552 / (184/27) = 552 * 27 / 184 = 3 * 27 = 81 men. Extra men = 81 - 56 = 25.