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 $80$ days. He works at it for $10$ days and then $B$ alone finishes the work in $42$ days. The two together could have completed the work in _________.
  1. $24\ days$
  2. $25\ days$
  3. $30\ days$
  4. $35\ days$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A does 1/80 per day. In 10 days, A does 10/80 = 1/8. Remaining work = 7/8. B does 7/8 in 42 days, so B does 1/48 per day. Together, they do 1/80 + 1/48 = (3+5)/240 = 8/240 = 1/30. They finish in 30 days.

Multiple choice

Kathy is a repair technician for a phone company. Each week, she receives a batch of phones that need repairs. The number of phones that she has left to fix at the end of each day can be estimated with the equation $P=108-23d$, where $P$ is the number of phones left and $d$ is the number of days she has worked that week. What is the meaning of the value $108$ in this equation?
  1. Kathy will complete the repairs within $108$ days
  2. Kathy starts each week with $108$ phones to fix
  3. Kathy repairs phones at a rate of $108$ per hour
  4. Kathy repairs phones at a rate of $108$ per day
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The equation P = 108 - 23d represents a linear function where 108 is the y-intercept, representing the starting value when d=0.

Multiple choice

A can do a work in x days and B can do the same work in y days then the number of days taken by A and B together to complete the work are
  1. $\displaystyle \frac{y}{x+y}$ days
  2. $\displaystyle \frac{x}{x+y}$ days
  3. $\displaystyle \frac{xy}{x+y}$ days
  4. $\displaystyle \frac{xy}{x-y}$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's rate is 1/x and B's rate is 1/y. Combined rate is (1/x + 1/y) = (x+y)/xy. The time taken is the reciprocal of the combined rate, which is xy/(x+y).

Multiple choice

$25$ students can do a job in $12$ days, but on the starting day, five of them informed thet they are not coming. By what fraction will the number of days required for doing the whole work get increased?
  1. $\dfrac35$
  2. $\dfrac37$
  3. $\dfrac34$
  4. $\dfrac14$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial work = 25 * 12 = 300 man-days. With 20 workers, days required = 300 / 20 = 15 days. The increase in days is 15 - 12 = 3 days. The fraction of increase is 3/12 = 1/4.

Multiple choice

A and B can do a piece of work together in 40 days Their skills of doing the work are in the ratio 8:5 How many days will A alone take to finish the same work if engaged alone?

  1. 52

  2. 104

  3. 64

  4. 65
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the daily work rates of A and B be 8x and 5x respectively, making their combined rate 13x. Since they complete the work together in 40 days, the total work is 13x * 40 = 520x. If A works alone, the time required is 520x / 8x = 65 days.

Multiple choice

$A$ and $B$ can do a piece of work in $8$ days. $B$ and $C$ can do the same work in $12$ days. If $A, B$ and $C$ can complete the same work in $6$ days, in how many days can $A$ and $C$ complete the same work?
  1. $8$ days
  2. $10$ days
  3. $6$ days
  4. $2$ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

1/A + 1/B = 1/8, 1/B + 1/C = 1/12, 1/A + 1/B + 1/C = 1/6. (1/A + 1/B + 1/C) - (1/B + 1/C) = 1/A = 1/6 - 1/12 = 1/12. (1/A + 1/B + 1/C) - (1/A + 1/B) = 1/C = 1/6 - 1/8 = 1/24. 1/A + 1/C = 1/12 + 1/24 = 3/24 = 1/8. So A and C take 8 days.