Today we are giving you the tricks to solve the problem related to time and work as well as pipe and cistern. Question-based on this topics are asked in many governments examinations. Questions are simple to solve by following the steps given in full article. Keep preparing for the exams because success comes from hard work.
Time and Work
- If A can do a piece of work in n days, then A's 1 day's work = 1/n
- If A's 1 day's work = 1/n, then A can finish the work in n days.
- If A is thrice as good a workman as B, then ratio of work done by A and B = 3:1
- If A is thrice as good a workman as B, the ratio of time taken by A and B to finish a work = 1:3
- Work and men are directly proportional to each other. i.e. more men means more work can be done in the same number of days
- Men and days are inversely proportional. i.e. More men means work will be done in a lesser number of days given that each man works equally.
- Work and days are directly proportional. i.e. More work can be done in more time given that each worker works equally.
If M1 men can do W1 work in D1 days working H1 hours per day and M2 men can do W2 work in D2 days working H2 hours per day (Where all the men work at the same rate), then:
M1 D1 H1/W1 = M1 D2 H2/W2
# Convert one work group to another:
a men or b women can do a piece of work then:
1 man = (b/a) women and,
1 Woman = (a/b) men
Questions and Answers
- A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then what is the fraction of the work left?
Ans: A's 1 day's work = 1/15
B's 1 day's work = 1/20
(A + B)'s 1 day's work = (1/15 + 1/20) = 7/60.
(A + B)'s 4 day's work = [(7/60) * 4] = 7/15.Therefore, Remaining work = (1 - 7/15) = 8/15.
- To complete a piece of work A and B take 8 days, B and C 12 days and A, B and C take 6 days. How man days A and C will takes to complete the same work.
(B + C)'s one day's work = 11/2
(A + B + C)'s 1 day's work = 1/6
Work done by A, alone:
= (A + B + C)'s 1 day's work - (B + C)'s one day's work
= 1/6 - 1/12 = 1/12
Work done by CC, alone:
= (A + B + C)'s 1 day's work - (A + B)'s one day's work
= 1/6 - 1/8 = 1/24
(A + C)'s one day's work:
= 1/12 + 1/24 = 1/8
(A + C) will take 8 days to complete the work together.
- Two pipes can fill the cistern in 10 hr and 12 hr respectively while the third empty it in 20 hr. If all pipes are opened simultaneously, then how many hours will it take to fill the cistern?
1/10 + 1/12 - 1/20 = 2/15
Hence, tank will be filled in 15/2 = 7.5 hour
- If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days. How much time taken by 15 men and 20 boys in doing the same type of work?
Then, 6x + 8y = 1/10 and 26x + 48y = 1/2.
Solving these two equations, we get : x = 1/100 and y = 1/200.
(15 men + 20 boy)'s 1 day's work
= 15/100 + 20/200 = 1/4.
15 men and 20 boys can do the work in 4 days.
- X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
Remaining work = 1 - 1/5 = 4/5.
(X + Y)'s 1 day's work = 1/20 + 1/12 = 8/60 = 2/15.
Now, 2/15 work is done by X and Y in 1 day.
So, 4/5 work will be done by X and Y in [15/2 x 4/5] = 6 days.
Hence, total time taken = (6 + 4) days = 10 days.
- Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?
= 3 * 11/60 = 11/20.
Part filled by C in 3 minutes = 3/10
Required ratio = [3/10 * 20/11] = 6/11.
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