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

16 men can do a piece of work in 16 days. 4 days after they started the work 8 more men joined them. How many days will they now take to complete the remaining work?
  1. $10\ days$
  2. $6\ days$
  3. $8\ days$
  4. $12\ days$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total work = 16 * 16 = 256 man-days. Work done in 4 days = 16 * 4 = 64 man-days. Remaining work = 256 - 64 = 192 man-days. New number of men = 16 + 8 = 24. Days to complete remaining work = 192 / 24 = 8 days.

Multiple choice

Choose the correct answer from the alternatives given. A contractor took a contract for building $12$ kilometre road in $15$ days and employed $100$ labours on the work. After $9$ days he found that only $5$ kilometre road had been constructed. How many more labours should be employed to ensure that the work may be completed with in the given time?
  1. $120$
  2. $90$
  3. $110$
  4. $100$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work done = 5km in 9 days with 100 men. Remaining work = 7km in 6 days. Using M1D1/W1 = M2D2/W2: (100 * 9) / 5 = (M2 * 6) / 7. 180 = (M2 * 6) / 7, so M2 = 210. Additional men = 210 - 100 = 110.

Multiple choice

A supplies $20$ men who work for $8$ hrs. a day working for $6$ days. $B$ supplies $15$ men working at $9$ hrs. a day for $7$ days and $C$ supplies $10$ men working $6$ hrs. a day for $8$ days to do a certain job. If Rs. $636$ is paid for all labour, what is $C's$ share?
  1. $130$
  2. $125$
  3. $128$
  4. $135$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Calculate man-hours: A = 20*8*6 = 960. B = 15*9*7 = 945. C = 10*6*8 = 480. Total = 960 + 945 + 480 = 2385. C's share = (480 / 2385) * 636 = 128.

Multiple choice

$4$ men and $3$ women finish a job in $6$ days. And $5$ men and $7$ women can do the same job in $4$ days. How long will $1$ man and $1$ woman take to do the work?
  1. $22\dfrac { 2 }{ 7 } days$
  2. $25\dfrac { 1 }{ 2 } days$
  3. $5\dfrac { 1 }{ 7 } days$
  4. $12 \dfrac { 7 }{ 22 } days$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let M and W be the daily work of a man and woman. 6(4M + 3W) = 1 (total work) => 24M + 18W = 1. 4(5M + 7W) = 1 => 20M + 28W = 1. Solving these, 4M = 10W => M = 2.5W. Substituting, 24(2.5W) + 18W = 1 => 78W = 1 => W = 1/78. Then M = 2.5/78 = 5/156. 1 man + 1 woman = 5/156 + 2/156 = 7/156. Time = 156/7 = 22 2/7 days.

Multiple choice

$16$ men can complete a work in $12$ days, $24$ children can complete the same work in $18$ days, $12$ men and $8$ children started working and after $8$ days, $3$ more children joined them. How many days will they now take to complete the remaining work ?
  1. $2$ days
  2. $4$ days
  3. $6$ days
  4. $8$ days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

16 men = 12 days, so 1 man = 192 days. 24 children = 18 days, so 1 child = 432 days. Daily work of 1 man = 1/192, 1 child = 1/432. 12 men + 8 children = 12/192 + 8/432 = 1/16 + 1/54 = 35/432. In 8 days, they do 8 * 35/432 = 35/54. Remaining work = 19/54. New force = 12 men + 11 children = 12/192 + 11/432 = 1/16 + 11/432 = 38/432 = 19/216. Days = (19/54) / (19/216) = 4 days.

Multiple choice

$A$ and $B$ can do a piece of work in $5$ days, $B$ and $C$ can do it in $7$ days. $A$ and $C$ can do it in $4$ days. Who among these will take the least time if put to do it alone ?
  1. $A$
  2. $B$
  3. $C$

  4. Data inadequate
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given (A+B)=1/5, (B+C)=1/7, (A+C)=1/4. Adding these gives 2(A+B+C) = 1/5+1/7+1/4 = 83/140, so (A+B+C) = 83/280. Subtracting (B+C) gives A = 83/280 - 40/280 = 43/280. Subtracting (A+C) gives B = 83/280 - 70/280 = 13/280. Subtracting (A+B) gives C = 83/280 - 56/280 = 27/280. Since A has the largest work rate (43/280), A takes the least time.

Multiple choice

$3$ men and $4$ boys can do a piece of work in $14$ days, while $4$ men and $6$ boys do the same work in $10$ days. How long would it take one man to finish the same work ?
  1. $40$ days
  2. $20$ days
  3. $35$ days
  4. $70$ 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. 14(3M + 4B) = 10(4M + 6B) => 42M + 56B = 40M + 60B => 2M = 4B => M = 2B. Total work = 14(3(2B) + 4B) = 14(10B) = 140B. Time for one man = 140B / M = 140B / 2B = 70 days.

Multiple choice

$A, B$ and $C$ complete a piece of work in $25, 20$ and $24$ days respectively. All work together for $2$ days and then $A$ and $B$ leave the work . $C$ works for next $\displaystyle8\frac{3}{5}$ days and then $A$ along with $D$ join $C$ and they all finish the work in next three days. In how many days $D$ alone can complete the whole work ?
  1. $22$ days
  2. $\displaystyle21\frac{1}{2}$days
  3. $23$ days
  4. $\displaystyle22\frac{1}{2}$days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work rates: A=1/25, B=1/20, C=1/24. Work done in 2 days by A, B, C: 2 * (1/25 + 1/20 + 1/24) = 2 * (24+30+25)/600 = 79/300. Remaining work = 221/300. C works for 43/5 days: 43/5 * 1/24 = 43/120. Remaining = 221/300 - 43/120 = (442-215)/600 = 227/600. A+D+C work for 3 days: 3 * (1/25 + 1/24 + 1/D) = 227/600. Solving for D gives 22.5 days.