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

$A$ and $B$ together can do a piece of work in 8 days. $B$ alone can do it in 12 days. $B$ alone works at it for 4 days. In how many more days after that could $A$ alone complete it.

  1. 15 days

  2. 18 days

  3. 16 days

  4. 20 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If A+B do the work in 8 days and B in 12 days, A's rate is 1/8 - 1/12 = 1/24 of the work per day. B works for 4 days, completing 4/12 = 1/3 of the work, leaving 2/3 of the work for A. A completes the remaining 2/3 at a rate of 1/24, taking (2/3) * 24 = 16 days.

Multiple choice

$A$ can cultivate $\displaystyle\frac{2}{5}$ of a land in 6 days and $B$ can cultivate $\displaystyle\frac{1}{3}$ of the same land in 10 days. Working together, $A$ and $B$ can cultivate $\displaystyle\frac{4}{5}$ of the land in:

  1. 4 days

  2. 5 days

  3. 8 days

  4. 10 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A cultivates 2/5 of the land in 6 days, so A's rate is (2/5)/6 = 1/15 land per day. B cultivates 1/3 of the land in 10 days, so B's rate is (1/3)/10 = 1/30 land per day. Together, their rate is 1/15 + 1/30 = 3/30 = 1/10 land per day; to cultivate 4/5 of the land, they need (4/5) / (1/10) = 8 days.

Multiple choice

$A$ and $B$ can do a piece of work in 30 days. While $B$ and $C$ can do the same work in 24 days and $C$ and $A$ in 20 days. They all work together for 10 days before $B$ and $C$ leave. How many days more will $A$ take to finish the work?

  1. 18 days

  2. 24 days

  3. 30 days

  4. 36 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Combined rates: A+B=1/30, B+C=1/24, C+A=1/20. Summing these gives 2(A+B+C) = 1/30+1/24+1/20 = 15/120 = 1/8, so A+B+C = 1/16. In 10 days, they do 10/16 = 5/8 of the work. Remaining work is 3/8. A's rate is (A+B+C) - (B+C) = 1/16 - 1/24 = 1/48. Time for A = (3/8) / (1/48) = 18 days.

Multiple choice

$A, B$ and $C$ can do a piece of work in 11 days, 20 days, and 55 days respectively working alone. How soon can the work be done if $A$ is assisted by $B$ and $C$ on alternate days?

  1. 7 days

  2. 8 days

  3. 9 days

  4. 10 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A = 1/11, B = 1/20, C = 1/55. Day 1: A works = 1/11. Day 2: A+B+C = 1/11 + 1/20 + 1/55 = (20 + 11 + 4)/220 = 35/220 = 7/44. Cycle (2 days) = 1/11 + 7/44 = 11/44 = 1/4. In 8 days (4 cycles), work = 4 * 1/4 = 1. Work done in 8 days.

Multiple choice

$40$ men can complete a work in $40$ days. They started working together. But $5$ men kept on leaving the job every $10th$ day. In how many days work will be completed ?
  1. $45$ days
  2. $50$ days
  3. $55.5$ days
  4. $56.66$ days

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

Work = 40 * 40 = 1600 man-days. Days 1-10: 40 men * 10 days = 400. Days 11-20: 35 men * 10 days = 350. Days 21-30: 30 men * 10 days = 300. Days 31-40: 25 men * 10 days = 250. Days 41-50: 20 men * 10 days = 200. Total so far = 1500. Remaining work = 100. Days 51 onwards: 15 men. 100/15 = 6.66 days. Total = 50 + 6.66 = 56.66.

Multiple choice

$X$ and $Y$ can do a piece of work in $30$ days. They work together for $6$ days and then $X$ quits and $Y$ finishes the work in $32$ more days. In how many days can $Y$ do the piece of work done?
  1. $30\ days$
  2. $32\ days$
  3. $10\ days$
  4. $40\ days$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

X+Y = 1/30 work/day. In 6 days, they do 6/30 = 1/5 work. Remaining = 4/5 work. Y does 4/5 work in 32 days, so Y's rate = (4/5) / 32 = 1/40 work/day. Y takes 40 days to finish the work.

Multiple choice

A. B and C together can do a piece of work in $40$ days. After working with B and C for $16$ days, A leaves and then B and C complete the remaining work in $40$ days more. A alone could do the work in
  1. $80$ days
  2. $90$ days
  3. $100$ days
  4. $120$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A, B, and C together complete 1/40 of the work per day. In 16 days they complete 2/5, leaving 3/5 for B and C, which they finish in 40 days, so their rate is 3/200 per day. A's rate is therefore 1/40 - 3/200 = 1/100, so A alone needs 100 days.

Multiple choice

A and B can together finish a work in $30$ days. They worked together for $20$ days and then B left. After another $20$ days A finished the remaining work. The number of days in which B alone can finish the work is
  1. $50$
  2. $48$
  3. $54$
  4. $60$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let A and B's work rates be a and b. Given 30(a+b) = 1 (total work). They worked together for 20 days: 20(a+b) = 2/3 of work. Remaining work 1/3 was done by A in 20 days, so A's rate is (1/3)/20 = 1/60. Since a+b = 1/30, then b = 1/30 - 1/60 = 1/60. Thus, B takes 60 days.

Multiple choice

Kim and Dominic can paint their apartment in $2$ days. Working alone, Kim can complete the job in $3$ days less than Dominic, working alone. How long would it take Kim to complete the painting, working alone?
  1. $3$ days
  2. $5$ days
  3. $4$ days

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let Dominic take x days. Kim takes x-3 days. 1/x + 1/(x-3) = 1/2. 2(x-3 + x) = x(x-3). 4x - 6 = x^2 - 3x. x^2 - 7x + 6 = 0. (x-6)(x-1) = 0. x=6. Kim takes 6-3 = 3 days.

Multiple choice

Mohan takes $16$ days less than Manoj to do a piece of work. If both working together can do it in $15$ days, in how many days will Mohan alone complete the work?
  1. $24\ days$
  2. $22\ days$
  3. $20\ days$
  4. $26\ days$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let Manoj take x days, Mohan takes x - 16 days. Together: 1/(x-16) + 1/x = 1/15. Solving this quadratic: x^2 - 46x + 240 = 0. Factors are (x-40)(x-6) = 0. Since x > 16, x = 40. Mohan = 40 - 16 = 24 days.