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

$A$ is $3$ times more efficient than $B$. Hence, he takes $60$ days less in painting a room. In how many days' work will the painting will be completed, if $A$ and $B$ both work together?
  1. $\displaystyle 30$ days
  2. $\displaystyle 45$ days
  3. $\displaystyle 22\frac{1}{2}$ days
  4. $\displaystyle 17\frac{1}{2}$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let B take x days, A takes x/3 days. x - x/3 = 60, so 2x/3 = 60, x = 90. A takes 30 days, B takes 90 days. Together: (30*90)/(30+90) = 2700/120 = 22.5 days.

Multiple choice

$2$ men and $5$ boys together can finish a piece of work in $4$ days, while $3$ men and $6$ boys can finish it in $3$ days. Find the time taken: i) by one man alone to finish the work ii) by one boy alone to finish the work.
  1. $18$ days and $36$ days
  2. $22$ days and $18$ days
  3. $11$ days and $13$ days
  4. $17$ days and $16$ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let M be work of one man, B be work of one boy. 4(2M + 5B) = 1, so 8M + 20B = 1. 3(3M + 6B) = 1, so 9M + 18B = 1. Solving the system: 72M + 180B = 9; 72M + 144B = 8. Subtracting: 36B = 1, so B = 1/36. 8M + 20/36 = 1, 8M = 16/36, M = 2/36 = 1/18. Man takes 18 days, boy takes 36 days.

Multiple choice

$X$ can do a piece of work in $24$ days, while $Y$ alone can do it in $16$ days. With the help of $Z$ they finish the work in $8$ days. Find in how many days $Z$ can do the work alone?
  1. $48$ days
  2. $36$ days
  3. $24$ days
  4. $12$ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Work done by X in 1 day = 1/24. Work done by Y in 1 day = 1/16. Work done by X+Y+Z in 1 day = 1/8. Work done by Z = 1/8 - (1/24 + 1/16) = 1/8 - (2/48 + 3/48) = 6/48 - 5/48 = 1/48. Z takes 48 days.

Multiple choice

$A$ can do a piece of work in $20$ days and $B$ in $40$ days. $A$ begins the work and there after they work alternately one on each day. On which day will the work be completed?
  1. $24$th day
  2. $25$th day
  3. $26$th day
  4. $27$th day
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A does 1/20 per day, B does 1/40 per day. In 2 days, they do 1/20 + 1/40 = 3/40. In 24 days (12 cycles), they do 12 * 3/40 = 36/40 = 9/10. On the 25th day, A does 1/20 (2/40), total 38/40. On the 26th day, B does 1/40, total 39/40. On the 27th day, A finishes the remaining 1/40.

Multiple choice

$A, B$ and $C$ can complete a work in $10, 12\ and\ 15$ days respectively. They started the work together, but $A$ left the work before 5 days of its completion. $B$ also left the work $2$ days after $A$ left. In how many days was the work completed.
  1. $4$
  2. $5$
  3. $7$
  4. $8$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let total work be 60 units. Rates: A=6, B=5, C=4. Let total days be T. A worked for T-5 days, B for T-2 days, C for T days. 6(T-5) + 5(T-2) + 4T = 60. 6T-30 + 5T-10 + 4T = 60. 15T = 100. T = 6.66. Checking the logic: If T=7, A works 2 days, B works 5 days, C works 7 days. 12+25+28 = 65. Close. Re-reading: A left 5 days before completion, B left 2 days after A (so 3 days before completion). 6(T-5) + 5(T-3) + 4T = 60. 15T = 60+30+15 = 105. T = 7.

Multiple choice

If $10$ men and $15$ women finish a work in $6$ days. One man alone finishes that work in $100$ days. In how many days will a women finish the work?
  1. $125$ days
  2. $150$ days
  3. $90$ days
  4. $225$ days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

1 man = 1/100 work/day. 10 men = 10/100 = 1/10 work/day. 10 men + 15 women = 1/6 work/day. 15 women = 1/6 - 1/10 = (5-3)/30 = 2/30 = 1/15 work/day. 1 woman = 1/(15*15) = 1/225 work/day. So 1 woman finishes in 225 days.

Multiple choice

X can do a piece of work in $8$ days and Y in $12$ days. When Z joined them, they completed the work in $3$ days. If the total money received for the work was $Rs. 400,$ what would be the share of X, based upon his proportionate output?
  1. $Rs. 200$
  2. $Rs. 160$
  3. $Rs. 150$
  4. $Rs. 170$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work rates: X=1/8, Y=1/12. Together in 3 days: 3(1/8 + 1/12 + Z) = 1. 3(5/24 + Z) = 1, so 5/24 + Z = 1/3, Z = 8/24 - 5/24 = 3/24 = 1/8. Since X and Z have the same rate (1/8), they do equal work. Total work is 3 days, X does 3/8 of the work. Share = (3/8) * 400 = 150.

Multiple choice

$A$ completes a work in $12$ days. $B$ completes the same work in $15$ days. $A$ started working alone and after $3$ days $B$ joined him. How many days will they now take together to complete the remaining work?
  1. $6$
  2. $8$
  3. $5$
  4. $4$

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's rate is 1/12, B's is 1/15. A works alone for 3 days, completing 3/12 = 1/4 of the work. Remaining work is 3/4. Combined rate is 1/12 + 1/15 = 9/60 = 3/20. Time taken = (3/4) / (3/20) = 5 days.