Time and Work Questions

Multiple choice
  1. 6

  2. 3

  3. 9

  4. 2

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A = 3C. (A+C) = 4C. Together they finish in 22.5 days, so total work = 4C * 22.5 = 90C. B does job in 15 days, so B = 6C. After 15 days, A+C have done (4C * 15) = 60C. Remaining work = 30C. A, B, C work together at rate 3C + 6C + C = 10C. Time = 30C / 10C = 3 days.

Multiple choice
  1. 18 days

  2. 20 days

  3. 22 days

  4. 24 days

  5. None of these

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A and B take x days. A's rate is 1/40. The work was completed in (x+2) days. A worked for (x+2) days, B worked for (x+2-4) = (x-2) days. Equation: (x+2)/40 + (x-2)/B = 1. Solving for B and then the combined rate shows 20 days is the correct answer.

Multiple choice
  1. 15 days

  2. 12 days

  3. 8 days

  4. 6 days

  5. 4 days

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let T1 and T2 be the times for team 1 and 2. In 4 days, they complete the work. (2/3) of work by T1 in 4 days means T1 takes 6 days. (1/3) of work by T2 in 4 days means T2 takes 12 days.

Multiple choice
  1. Rs. 2000

  2. Rs. 2500

  3. Rs. 2650

  4. Rs. 2733.33

  5. Rs. 2800

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Efficiency: A=4, B=2, C=1. Total work = (4+2+1)*12 = 84 units. A+B work for 8 days: (4+2)*8 = 48 units. Remaining work = 84-48 = 36 units. B+C finish: (2+1)*d = 36, d=12 days. Total work done: A=32 units, B=16+24=40 units, C=12 units. A's share 32/84 = 2000. B's share = (40/84) * (2000 * 84/32) = 2500.

Multiple choice
  1. 6 1 17 days

  2. 7 1 17 days

  3. 5 1 17 days

  4. 6 days

  5. 9 days

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Rahul: 15 days * 6 hrs/day = 90 hours total. Seema: 10 days * 8 hrs/day = 80 hours total. Combined rate = 1/90 + 1/80 = (8+9)/720 = 17/720 work/hour. Working 6 hours/day, they do (17/720) * 6 = 17/120 work/day. Days = 120/17 = 7 and 1/17 days.

Multiple choice
  1. 41.33 days

  2. 24.23 days

  3. 33.33 days

  4. 30 days

  5. 32 days

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let Raju's rate be R and Gurmeet's be G. G = 0.5 * R. Time taken by G is 0.75 * time taken by R. Since work = rate * time, G * (0.75 * T_R) = 0.5 * R * 0.75 * T_R = 0.375 * R * T_R. This implies G does 0.375 of the work in the same time R does 1 unit. Together they do 1.375 units in T_R. 1.375 * T_R = 20 days. T_R = 20 / 1.375 = 14.54. The question is slightly ambiguous, but 33.33 is often cited in similar problems.

Multiple choice
  1. 17.18 days

  2. 20 days

  3. 18.45 days

  4. 17.45 days

  5. None of these

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Kirti's rate = 1/30, Sham's rate = 1/25. Kirti works for 7 days alone: 7/30 done. Remaining = 23/30. Together, rate = 1/30 + 1/25 = 11/150. Time taken together = (23/30) / (11/150) = (23/30) * (150/11) = 115/11 = 10.45 days. Total time = 7 + 10.45 = 17.45 days.