| 1. Machine P can produce 2000 units in 3 hours and 20 minutes, and Machine Q can produce 2000 units in 8 hours. In how many hours can Machines P and Q, working together at these constant rates, produce 8500 units? | Easy |
| A. 12 hours B. 10 hours C. 8 hours D. None of these |
View Answer
Answer: Option B
Explanation:
In 1 hour, Machine P produces (2000/(10/3)) = 600 units
In 1 hour, Machine Q produces (2000/8) = 250 units
In an hour, Machines P and Q together produce (600+250 = 850) units
Thus 8500 units are produced by them in (8500/850 =10) hours.
| 2. If Peter and Robert can do a job in 3 days when working together at their respective constant rates, and Peter alone can do the job in 9 days, in how many days can Robert alone do it? | Easy |
| A. 6 days B. 4 days C. 4.5 days D. None of these |
View Answer
Answer: Option C
Explanation:
1/9+1/R=1/3
(R+9)/9R=1/3
-> R = 4.5 days
Working alone, Robert can do the job in 4.5 days.
| 3. Alex does a job in 4 days, Brad does it in 6 days, and Charles does the job in 8 days. They all work together for a day, and then Charles leaves. In how many days can the remaining work be completed by Alex and Brad? | Medium |
| A. 11/10 days B. 12/11 days C. 11/9 days D. None of these |
View Answer
Answer: Option A
Explanation:
Alex does 1/4 of the job in 1 day.
Brad does 1/6 of the job in a day.
Charles does 1/8 of the job in 1 day.
∴ If they work together, in one day they would do (1/4) + (1/6) + (1/8) = 13/24 of the total job.
Work left after the first day = 1 –(13/24) = 11/24
Now, in 1 day Alex and Brad do (1/4)+(1/6) = 5/12 of the job.
They will do 11/24 of the job in (12/5) * (11/24) = 11/10 days
| 4. A job can be completed in 20 days by 6 men and 4 women. The men work 8 hours and the women 5.5 hours per day, and 2 women do as much work in an hour as 1 man. How many hours would it take for one man, working alone, to complete the job? | Medium |
| A. 1770 hours B. 590 hours C. 1180 hours D. None of these |
View Answer
Answer: Option C
Explanation:
Given, 6 men + 4 women take 20 days to complete the work.
Now, each man works 8 hours per day
-> 6 men will put in 48 hours per day
-> 6 men will put in 48*20 = 960 man hours in 20 days.
Further, 2 women ≅ 1 man (in terms of work efficiency)
-> 4 women ≅ 2 men
-> 4 women or 2 men working 5.5 hours per day will put in 11 man hours per day.
-> 4 women or 2 men will put in 11*20 =220 man hours in 20 days.
Therefore, total man hours required for completing the work = 960+220 = 1180
-> 1 man, working alone, will take 1180 hours to complete the work.
| 5. 4 men and 14 women complete a certain job in 8 days, while 6 men and 16 women complete the same job in 6 days. In how many days will 28 men and 8 women complete a job thrice as big? | Medium |
| A. 3 days B. 8 days C. 6 days D. None of these |
View Answer
Answer: Option C
Explanation:
Given, 4M + 14W take 8 days & 6M + 16W take 6 days to complete the work.
Let 1M ≅ nW
-> (4n+14)*8 = (6n+16)*6
-> n = 4
-> 1M ≅ 4W
In terms of work efficiency, 4M + 14W ≅ 30W (from above)
-> 30W take 8 days or 1W takes 30*8 = 240 days
Further, 28M + 8W = 120W
-> 120W will take 240/120 = 2 days to complete the work.
Thus, 120W will take 3*2 = 6 days to complete a piece of work thrice as big.
| 6. 20 oxen or 30 sheep can graze a field in 20 days. In how many days will 60 oxen and 60 sheep graze it? | Easy |
| A. 6 days B. 4 days C. 8 days D. None of these |
View Answer
Answer: Option B
Explanation:
Given, 20 oxen ≅ 30 sheep, and 20 oxen (or 30 sheep) take 20 days.
Now, 60 oxen + 60 sheep ≅ 150 sheep
30 sheep take 20 days to graze.
-> 1 sheep will take 30*20 days.
-> 150 sheep will take (30*20)/150 = 4 days
| 7. Eight cats kill eight rats in eight days. In how many days will 32 cats kill 32 rats? | Easy |
| A. 8 days B. 32 days C. 24 days D. None of these |
View Answer
Answer: Option A
Explanation:
Given, 8C kill 8R in 8 days.
-> 8C kill 1R in (8/8) days.
-> 1C kills 1R in (8/8)*8 = 8 days
-> 1C kills 32R in (8*32) days
-> 32C kill 32R in (8*32)/32 = 8 days
| 8. Alex and Brad can do a piece of work in 8/7 days; Brad and Charles can do it in 4/3 days; Alex and Charles can do it in 3/2 days. In how many days will Alex, Brad and Charles finish a piece of work which is 55 times as big if they work together? | Easy |
| A. 48 B. 36 C. 24 D. None of these |
View Answer
Answer: Option A
Explanation:
Let a, b, c be the number of days Alex, Brad and Charles take to do the job if working alone. Thus,
1/a + 1/b = 1/(8/7) = 7/8 —– ❶
1/b + 1/c = 1/(4/3) = 3/4 —– ❷
1/a + 1/c = 1/(3/2) = 2/3 —– ❸
Adding all 3 equations
2[1/a + 1/b + 1/c] = [7/8 + 3/4 + 2/3]
-> 1/a + 1/b + 1/c = 110/96 = 55/48
-> Alex, Brad, Charles together would take 48/55 days to complete the work.
-> They will take 48 days to complete a piece of work 55 times as big.
| 9. A pipe X can drain a tank in 8 hours and another pipe Y can fill the empty tank in 4 hours. If N1 pipes of type X, and N2 pipes of type Y are opened simultaneously, the tank gets filled in 2 hours. Which of the following is NOT a possible value of N1 and (N1 + N2) respectively? | Difficult |
| A. 6, 11 B. 8, 14 C. 10, 18 D. 14, 23 |
View Answer
Answer: Option C
Explanation:
Pipe X drains the tank in 8 hours.
-> In 1 hour, it drains 1/8th of the tank.
-> In 1 hour, N1 such pipes, drain N1/8 of the tank.
Pipe Y fills the tank in 4 hours.
-> In 1 hour, it fills 1/4th of the tank.
-> In I hour, N2 such pipes fill N2/4 of the tank.
If N1 & N2 pipes are opened simultaneously, then in 1 hour the portion which gets filled = (N2/4)-(N1/8) =1/2
-> 2N2 = N1 +4
-> N2 = (N1/2) +2 —– ❶
N1 and N2 have to be positive integers -> N1 has to be a multiple of 2; let it be 2k (where k is a positive integer).
-> N2 = k+2 —– ❷
-> N1 + N2 = 2k+k+2 = 3k+2 —– ❸
Thus, N1 has to be an even number, and N1+N2 has to be of the form 3k+2, such that N2 = (N1/2) +2
From the given options, only option C does not satisfy the conditions ❶, ❷ and ❸.
| 10. Two pipes X and Y fill a vessel completely in 4 min and 5 min respectively. There is a leak at the vessel’s side at a height of p cm from the top. The total height of the vessel is q cm [p/q = ½]. The leak empties the contents of the vessel above it in 8 minutes. The vessel gets full in k minutes. Which of the following is true for k? | Difficult |
| A. 2.25 < k < 2.5 B. 2.5 < k < 2.75 C. 2 < k < 2.25 D. None of these |
View Answer
Answer: Option A
Explanation:
Assume there is no leak, and that the complete vessel gets filled in t mins.
-> 1/4+ 1/5 = 1/t
-> t = 20/9 min
Therefore, the portion below the leak would get filled in 1/2(20/9) = 10/9 mins (because the portion below the leak is half the vessel)….❶
Pipes X and Y would take 2 min and 2.5 min respectively to fill half the vessel. Let the time taken to fill the vessel above the leak be m minutes.
-> 1/2 + 1/2.5 – 1/8 = 1/m
-> m = 200/155 = 40/31 mins ……..❷
From ❶ and ❷, total time, k = 10/9 + 40/31 = 2.4 minutes