Time and Work problems
- 1. P can do a piece of work in 5 less days than Q. If both of them can do the same work in 1119 days, in how many days will Q alone do the same work ?
Options- A. 24 days
- B. 25 days
- C. 20 days
- D. 19 days Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 25 days
Explanation:
Let Q complete that work in 'L' days
=>
=>
L = 25 days.
- 2. X can complete the work in 10 days, Y can do the same in 15 days. If they are hired for 5 days to do the work together, what is the work that left unfinished?
Options- A. 1/3
- B. 2/3
- C. 1/6
- D. 5/6 Also asked in: AIEEE, Bank PO, Bank Clerk, GATE, CAT, Bank Exams
Correct Answer: 1/6
Explanation:
Given X can do in 10 days
=> 1 day work of X = 1/10
Y can do in 15 days
=> 1 day work of Y = 1/15
1day work of (X + Y) = 1/10 + 1/15 = 1/6
Given they are hired for 5 days
=> 5 days work of (X + Y) = 5 x 1/6 = 5/6
Therefore, Unfinished work = 1 - 5/6 = 1/6
- 3. Three men, four women and six children can complete a work in 9 days. A women does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 9 days?
Options- A. 7
- B. 8
- C. 9
- D. 6 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO, Database Administrator, IT Trainer
Correct Answer: 7
Explanation:
Given (3 Men + 4 Women + 6 Children) -----> 9 days
But W = 2M and C = M/2
Now, convert Men and Children into Women by
Therefore, 7 women alone can complete this work in 9 days.
- 4. A can complete 9/10 part of a work in 31 days. After that, with the help of B he can complete the remaining work in 4 days. In how many days will A and B together can complete that work ?
Options- A. 36
- B. 40
- C. 42
- D. 38 Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 40
Explanation:
Remaining work = 1 - 9/10 = 1/10
=> A & B together completes 1/10 of work in 4 days
=> 1 work can completed in ------ ? days
Let it be x days
=>
=> x = 40 days.
Hence, A & B together can complete the work in 40 days.
- 5. Twenty men can do a work in eighteen days. Eighteen women can complete the same work in fifteen days. What is the ratio between the capacity of a woman and a man ?
Options- A. 4:5
- B. 3:4
- C. 4:3
- D. 2:3 Also asked in: GATE, CAT, Bank Exams, Bank PO, Bank Clerk
Correct Answer: 4:3
Explanation:
(20 x 18) men can complete the work in in one day.
one man's one day work = 1/360
(18 x 15) women can complete the work in 1 day
1 woman's one day work = 1/270
So, required ratio = = 4:3
- 6. 16 men and 12 women can complete a work in 20 days. 18 women can complete the same work in 40 days. In how many days will 12 men 27 women complete the same work?
Options- A. 16 days
- B. 18 days
- C. 19 days
- D. 21 days Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 16 days
Explanation:
(16M + 12W) x 20 = 18W x 40
=> 2M = 3W
Then,
Convert all men into women
12M + 27W = 27 + 12 x 3/2W = 45W
Let number of days required be 'D'
=> 18 x 40 = 45 x D
=> D = 16 days.
- 7. A tank has an inlet and outlet pipe. The inlet pipe fills the tank completely in 2 hours when the outlet pipe is plugged. The outlet pipe empties the tank completely in 6 hours when the inlet pipe is pluggeed. If there is a lekage also which is capable of draining out the liquid from the tank at half of the rate of outet pipe,them what is the time taken to fill the emty tank when both the pipes are opened?
Options- A. 3 hours
- B. 4 hours
- C. 5 hours
- D. None of these Discuss
Correct Answer: 4 hours
Explanation:
Rate of leakage = 8.33% per hour
Net efficiency = 50 - (16.66 + 8.33)= 25%
Time required = 100/25 = 4 hours
- 8. 28 Men and 52 women working together completes a work in 22.5 days. 35 men and 65 women working together on same work will complete it in how many days?
Options- A. 16
- B. 18
- C. 19
- D. 21 Also asked in: CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 18
Explanation:
Clearly total persons are increased in 28/35 :: 52/65 = 4:5.
As time is inversely proportional to men, so total time will decrease in the ratio 5:4.
Hence, 22.5 x 4/5 = 18 days.
- 9. In a hostel, there was food for 1000 students for one month. After 10 days, 1000 more students joined the hostel. How long would the students be able to carry on with the remaining food?
Options- A. 10 days
- B. 15 days
- C. 20 days
- D. 5 days Also asked in: GATE, CAT, Bank Exams, Bank PO, Bank Clerk
Correct Answer: 10 days
Explanation:
After 10 days, the remaining food would be sufficient for the 1000 students for 20 more days
-->If 1000 more students are added, it shall be sufficient for only 10 days (as the no. of students is doubled, the days are halved).
- 10. 50 men can build a tank in 40days, but though they begin the work together, 5 men quit every ten days. The time needed to build the tank is ?
Options- A. 50 days
- B. 48 days
- C. 47.5 days
- D. 49 days Also asked in: GATE, CAT, Bank Exams, Bank PO, Bank Clerk
Correct Answer: 50 days
Explanation:
50 men can build a tank in 40 days
Assume 1 man does 1 unit of work in 1 day
Then the total work is 50×40 = 2000 units
50 men work in the first 10 days and completes 50×10 = 500 units of work
45 men work in the next 10 days and completes 45×10 = 450 units of work
40 men work in the next 10 days and completes 40×10 = 400 units of work
35 men work in the next 10 days and completes 35×10 = 350 units of work
So far 500 + 450 + 400 + 350 = 1700 units of work is completed and
Remaining work is 2000 - 1700 = 300 units
30 men work in the next 10 days. In each day, they does 30 units of work.
Therefore, additional days required = 300/30 =10
Thus, total 10+10+10+10+10 = 50 days required.
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