Quantitative Aptitude

Time and Work

2,195 Questions
All Pairwise rates and staged schedules 440 Workers-days-hours chain rule 439 LCM units and efficiency ratios 409 Different worker categories 311 Combined rates and an unknown worker 257 Division of wages 219 Alternate work 110 Opposing rates 10

Time and Work Questions

Multiple choice

A can do a piece of work in 12 days and B alone can do it in 16 days. They worked together on it for 3 days and then. A left. how long B take to finish the remaning work?
  1. $8$ days
  2. $5$ days
  3. $7$ days
  4. $9$ days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A's rate = 1/12, B's rate = 1/16. Combined rate = 1/12 + 1/16 = 7/48. In 3 days, they do 3 * (7/48) = 21/48 = 7/16 of the work. Remaining work = 1 - 7/16 = 9/16. B takes (9/16) / (1/16) = 9 days to finish.

Multiple choice

Two men and $7$ children complete a certain piece of work in $4$ days while $4$ men and $4$ children complete the same work in only $3$ days. The number of days required by $1$ man to complete the work is
  1. $60$ days
  2. $15$ days
  3. $6$ days
  4. $51$ days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let M be the work of a man and C be the work of a child per day. From the problem, 2M + 7C = 1/4 and 4M + 4C = 1/3. Solving this system gives M = 1/15, meaning one man completes the work in 15 days.

Multiple choice

If one man or two women or three boys can do a piece of work in 22 days, then the same piece of work will be done by 1 man, 1 boy and 1 woman in
  1. $8$ days
  2. $12$ days
  3. $6$ days
  4. $11$ days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If 1 man, 2 women, or 3 boys take 22 days, their daily work rates are 1/22, 1/44, and 1/66 of the total work respectively. The combined rate of 1 man, 1 woman, and 1 boy is (1/22 + 1/44 + 1/66) = (6+3+2)/132 = 11/132 = 1/12. Thus, they complete the work in 12 days.

Multiple choice

$A$ and $B$ together can complete a work in 12 days. $A$ alone can complete it in 20 days. If $B$ does the work only for half a day daily, then in how many days will $A$ and $B$ together complete the work?
  1. $10$ days
  2. $11$ days
  3. $15$ days
  4. $20$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A+B = 1/12, A = 1/20. So B = 1/12 - 1/20 = (5-3)/60 = 2/60 = 1/30. If B works half-time, his rate is 1/60. Combined rate = 1/20 + 1/60 = 4/60 = 1/15. Time taken = 15 days.

Multiple choice

Choose the most appropriate option. Two men and seven boys can do a work in $14$ days. Three men and eight boys can do the same work in $11$ days. Further eight men and six boys can do three times the amount of this work in:
  1. $18$ days
  2. $30$ days
  3. $24$ days
  4. $21$ days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let M be the work of a man and B be the work of a boy per day. From the equations 14(2M + 7B) = W and 11(3M + 8B) = W, we find 28M + 98B = 33M + 88B, which simplifies to 5M = 10B or M = 2B. Substituting M = 2B into the first equation, 14(4B + 7B) = 154B = W. For 8M + 6B, we have 8(2B) + 6B = 22B. The time required for 3W is (3 * 154B) / 22B = 21 days.

Multiple choice

Choose the correct answer from the alternatives given : Working together A and B can finish a piece of work in 5 days. If working speed of A was doubled and working speed of B reduced to half the same work was done in 4 days. In how many days can A finish the work alone.
  1. $10$ days
  2. $12$ days
  3. $15$ days
  4. $8$ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A and B's rates be a and b. 1/a + 1/b = 1/5. If A is 2a and B is b/2, 1/(2a) + 1/(b/2) = 1/4, which is 1/(2a) + 2/b = 1/4. Solving the system: 1/a + 1/b = 1/5 and 1/(2a) + 2/b = 1/4. Multiply first by 2: 2/a + 2/b = 2/5. Subtract second: 1.5/a = 2/5 - 1/4 = 3/20. So 1/a = (3/20) * (2/3) = 1/10. A takes 10 days.

Multiple choice

Choose the correct answer from the alternatives given. 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can finish it in 8 days. Number of days taken by 2 men and I boy to finish it will be
  1. 13$\dfrac{1}{2}$ days
  2. $13$ days
  3. 12 $\dfrac{1}{2}$days
  4. $14$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let M be men's daily work and B be boys' daily work. 10(2M + 3B) = 1, so 2M + 3B = 0.1. 8(3M + 2B) = 1, so 3M + 2B = 0.125. Solving the system: M = 0.0375, B = 0.00833. For 2M + 1B, work per day = 2(0.0375) + 0.00833 = 0.0833. Days = 1 / 0.0833 = 12.5 days.

Multiple choice

If 2 men and 3 boys can do a piece of work in 10 days and 3 men and 2 boys can do it 8 days, how long will 2 men and 1 boy take to do it

  1. 15

  2. 18

  3. 12.5

  4. 16
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let M be the work of a man and B be the work of a boy per day. 10(2M + 3B) = 1, so 20M + 30B = 1. 8(3M + 2B) = 1, so 24M + 16B = 1. Solving the system: 80M + 120B = 4 and 180M + 120B = 7.5. Subtracting gives 100M = 3.5, M = 0.035. Then 30B = 1 - 20(0.035) = 0.3, B = 0.01. 2M + 1B = 2(0.035) + 0.01 = 0.08. Time = 1 / 0.08 = 12.5 days.

Multiple choice

A contractor Abhay Singh employed some men to do a piece of work which can be done by 16 men in 14 days.At the end of 5 days, 7 of the men stopped working and 3 days later half of the remainder stopped working; the rest finished the work in 5 days.What is the number of men originally employed?
  1. $25$
  2. $27$
  3. $29$
  4. $33$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x be the number of men. Total work = 16 * 14 = 224 man-days. Work done in first 5 days = 5x. Remaining work = 224 - 5x. After 7 men leave, x-7 men work for 3 days. Then (x-7)/2 men work for 5 days. Setting up the equation: 5x + 3(x-7) + 5((x-7)/2) = 224. Solving this yields x = 25.

Multiple choice

$A$ is three times more efficient worker than $B$ and is therefore able to complete a work in $60$ days less than $B$. What is the number of days that $A$ and $B$ together will take to complete the work?
  1. $22.5$ days
  2. $22$ days
  3. $24.5$ days
  4. $24$ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Efficiency ratio A:B = 3:1. Time ratio A:B = 1:3. Let A take x days, B takes 3x days. 3x - x = 60 -> 2x = 60 -> x = 30. A takes 30 days, B takes 90 days. Combined rate = 1/30 + 1/90 = 4/90 = 2/45. Time = 45/2 = 22.5 days.