Even after the perfect preparation of Time and Work concepts, are you still worried about the exam? If yes, then stop your worry now! Here we are providing the Worksheet on Time and Work so that you can practice more and prepare well for the exam. You can use this as one last time revision material to test your caliber of answering the questions. Go through the below sections, to check Time and Work Problems, and important questions.
It is mandatory for every student to check themselves before going to the exam. That can also be possible with a lot of practice. The below-given questions will help you to check your capability of solving the questions at a specific time.
1. The time required for X to complete the job is 9 hours each day for 7 days and the time required for Y to complete the same job is 7 hours each day for 6 days. If both X and Y work together for 42/5 hours each day, how many days would it take to complete the whole job?
A. 3 Days
B. 7 Days
C. 8 Days
D. 6 Days
A (3 Days)
X completes the work in (7*9) = 63 hours
Y completes the work in (6*7) = 42 hours
X’s 1 hour’s work = 1/63 and Y’s 1 hour’s work = 1/42
(X+Y)’s 1 hour’s work = (1/63+1/42) = 5/126
Both X and Y will finish the work in (126/5) hours
Number of days of 42/5 hours each = (126/5 * 5/42) = 3 days
2. X and Y complete a piece of work in 18 days, Y and Z complete the same work in 24 days, X and Z complete it in 36 days. How many days will X, Y, and Z take to finish it, working together and separately?
A. Together = 14, X = 68 Days, Y = 166/5 Days, Z = 166 Days
B. Together = 16, X = 48 Days, Y = 144/5 Days, Z = 144 Days
C. Together = 24, X = 64 Days, Y = 166/5 Days, Z = 166 Days
D. Together = 20, X = 36 Days, Y = 154/5 Days, Z = 154 Days
B (Together = 16, X = 48 Days, Y = 144/5 Days, Z = 144 Days)
(X+Y)’s 1 day work = 1/18, (Y+Z) one day’s work = 1/24 and (X+Z)’s 1 day’s work = 1/36
Adding we get: 2 (X+Y+Z)’s 1 day’s work =(1/18+1/24+1/36) = 9/72 = 1/8
(X+Y+Z)’s 1 day’s work = 1/16
Thus, X, Y and Z together can finish the job in 16 days.
Now, X’s 1-day work = [(X+Y+Z)’s 1 day work] – [(Y+Z)’s 1 day work] = (1/16-1/24) = 1/48
X alone can finish the job in 48 days.
Similarly, Y’s 1 day work = (1/16 – 1/36) = 5/144
Y alone can finish the job in 144/5
And Z’s 1 day work = (1/16-1/18) = 1/144
Z alone can finish the job in 144 days.
3. X is twice as good a workman as Y and together they finish a piece of job in 18 days. How many days will X alone take finish the work?
A. 40 Days
B. 27 Days
C. 15 Days
D. 30 Days
B (27 Days)
(X’s 1 day’s work): (Y’s 1 day’s work) = 2:1
(X+Y)’s 1 day’s work = 1/18
Divide 1/18 in the ratio 2:1
X’s 1 day’s work =(1/18*2/3) = 1/27
Hence, X alone can finish the work in 27 days.
4. X and Y can together complete a piece of job in 4 days. If X alone can complete the same job in 12 days, in how many days can Y alone complete that work?
A. 6 Days
B. 8 Days
C. 10 Days
D. 4 Days
A (6 Days)
(X+Y)’s 1 day’s work = 1/4, X’s 1 day’s work = 1/12
Y’s 1 day’s work = (1/4-1/12) = 1/6
Hence, Y alone can complete the work in 6 days.
5. Suppose, X can finish a particular job in 12 days. Y is 60% more efficient than X. How days will Y take to complete the work?
A. 14/3 Days
B. 15/2 Days
C. 28/3 Days
D. 15/4 Days
B (15/2 Days)
The ratio of times taken by X : Y = 160 : 100 = 8 : 5
Suppose Y alone takes x days to do the job.
Then, 8 : 5 :: 12 : x = 8x = 5*12
x=7 1/2 days
6. The time required for X to complete the work in 80 days. X works it for 10 days and then Y takes 42 Days to finish the work alone. How much time do X and Y take to complete the whole work when working together?
A. 50 Days
B. 40 Days
C. 30 Days
D. 15 Days
C (30 Days)
Work done by X in 10 days = (1/80 * 10) = 1/8
Remaining work = (1-1/8) = 7/8
Now, 7/8 work is done by Y in 42 days
The whole work will be done by Y in (42*8/7) = 48 days
X’s 1 day’s work = 1/80 and Y’s 1day’s work = 1/48
(X+Y)’s 1 day’s work = (1/80+1/48) = 8/240 = 1/30
Hence X and Y both will finish the work in 30 days
7. X takes 10 days less than the time taken by Y to finish a piece of work. If X and Y can do it in 12 days, then how much time will Y alone take to finish the job?
A (30 Days)
As mentioned in the question, X and Y can complete the work in 12 days.
We Suppose that X takes 24 days and Y takes 24 days to complete the work.
But it is given that X takes less no of days when compared to Y
Now, look at the option as it is mentioned that Y takes more no. of days than X, the answer should be more than 24.
So, we can cancel option C and option D is also approximately equal to 25 so we can cancel it.
Now we go for the trial and error method with the remaining 2 options.
Let’s take option A(30), so according to the question if Y takes 30 Days, X takes 10 days less i.e., 20 Days
That is X takes 2 portions and Y takes 3 portions. If we calculate = 60/5 = 12 days.
So 30 days is the answer.
8. If 3 men or 4 women can do a piece of work in 43 days, how long will 7 men and 5 women take to do the same work?
A. 10 days
B. 11 days
C. 9 days
D. 12 days
As mentioned in the question, 3 men and 4 women can do the work in 43 days
Here we can assume that 3 men can do the work in 43 days or 4 women also can do the work in 43 days
Here we need to find how many days 7 men and 5 women would need to complete the same work.
Here, we need to observe that the question is in the form of “or” followed by “and”, so here is an easy technique to follow the solution.
If there is a condition like “or”, the number of days would be the same and they will ask us to find something in a type of relation “and”.
To find the number of days, Multiply the numbers which you have in question 4*3*43. This will be our numerator value.
For the denominator, multiply the value of men and women and add them to the value of women and men (men*women)+(women*men)
Divide the numerator to the denominator and you will get the number days value as 12 days which will be your final answer.