Time and Work Questions

Multiple choice
  1. 4

  2. 6

  3. 8

  4. None of these

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

Work rates: A+B+C = 1/10, A = 1/24, B = 1/30. C = 1/10 - (1/24 + 1/30) = 1/10 - (5+4)/120 = 1/10 - 9/120 = 12/120 - 9/120 = 3/120 = 1/40. A+B work for 12 days: (1/24 + 1/30) * 12 = (9/120) * 12 = 9/10. Remaining work = 1/10. C takes (1/10) / (1/40) = 4 days.

Multiple choice
  1. 10

  2. 15

  3. 18

  4. 20

  5. 24

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

Let B's rate be 1/x. A's rate = 1/30. Scheduled time T = 1 / (1/30 + 1/x) = 30x / (x+30). Actual time = T+1. Work done: (A+B) worked for (T+1)/2 - 1.5 days, then B worked alone for 3 days, then (A+B) finished. This is complex. Let's use: (A+B) worked for T+1 days total, but A was absent for 3 days. So A worked for (T+1) - 3 = T-2 days. B worked for T+1 days. (T-2)/30 + (T+1)/x = 1. Substitute T = 30x/(x+30). Solving this leads to x=15.

Multiple choice
  1. Rs. 60

  2. Rs. 20

  3. Rs. 40

  4. Rs. 80

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

Work done by A in 3 days = 3/5. Work done by B in 3 days = 3/8. Work done by C and D = 1 - (3/5 + 3/8) = 1 - (24+15)/40 = 1 - 39/40 = 1/40. C = 2D, so 3D = 1/40, D = 1/120. Share of D = (1/120) * 4800 = 40.

Multiple choice
  1. 14

  2. 15

  3. 10

  4. 12

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

Aditi's total required time is 240 hours, and Kavya's is 160 hours, meaning their hourly work rates are 1/240 and 1/160 of the project, respectively. Under the collaboration terms, if Aditi works 4 hours a day for 2D days, and Kavya works 8 hours a day for D days, the sum of their work is (8D / 240) + (8D / 160) = 1. Solving this equation gives D = 12 days for Kavya.

Multiple choice
  1. 18 21 35 days

  2. 18 31 35 days

  3. 19 31 35 days

  4. 19 21 35 days

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

LCM(24, 30, 32) = 480. Rates: A=20, B=16, C=15. Day 1 (A+C): 20+15=35. Day 2 (B): 16. Cycle of 2 days = 51 units. 480 / 51 = 9 full cycles (18 days) = 459 units. Remaining = 21 units. Day 19 (A+C) completes 35 units, so 21/35 = 3/5 of a day. Total = 18 + 3/5 = 18 3/5 days. The option 18 21/35 is equivalent to 18 3/5.

Multiple choice
  1. 4 X Y + 1 is an even integer.

  2. 2X + Y = 22

  3. X - Y is an odd integer.

  4. X2 + 1 is a multiple of 13.

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

Kamla's rate = 1/24, Nirmala's rate = 1/18. Kamla works X days, Nirmala works Y days. X + Y = 20. Work done = X/24 + Y/18 = 1. Multiply by 72: 3X + 4Y = 72. Substitute Y = 20 - X: 3X + 4(20 - X) = 72, so 3X + 80 - 4X = 72, X = 8. Then Y = 12. Check options: X^2 + 1 = 64 + 1 = 65, which is 5 * 13.

Multiple choice
  1. 6.5 days

  2. 6 days

  3. 5 days

  4. 5.5 days

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

Let King's efficiency be 1 unit/day. Kong = 2 units/day. Kim = 4 * 2 = 8 units/day. Total efficiency = 1 + 2 + 8 = 11 units/day. Total work = 11 * 4 = 44 units. Kim's time = 44 / 8 = 5.5 days.