Easy Level
These questions are targeted to improve your knowledge of basic concepts, though easy questions are rare in CAT. These are extremely important for conceptual understanding at the foundation level. Try this question by yourself:
Question for Practice Questions: Time & Work
Try yourself:A can do a piece of work in 10 days and B can do the same work in 20 days. With the help of C, they finish the work in 5 days. How long will it take for C alone to finish the work?
Explanation
Step 1: Work Rate of A and B
A can do the work in 10 days, so A's work rate is:
Rate of A = 1/10 work/day.
B can do the work in 20 days, so B's work rate is:
Rate of B = 1/20 work/day.
Step 2: Combined Work Rate of A, B, and C
Together, A, B, and C finish the work in 5 days. Their combined work rate is:
Rate of A + Rate of B + Rate of C = 1/5 work/day.
Step 3: Total Work Rate of A and B
The combined work rate of A and B is:
Rate of A + Rate of B = 1/10 + 1/20.
Finding the sum:
1/10 + 1/20 = 2/20 + 1/20 = 3/20.
Step 4: Work Rate of C
Using the combined rate of A, B, and C:
Rate of C = Rate of A + Rate of B + Rate of C - Rate of A + Rate of B.
Rate of C = 1/5 - 3/20.
Converting to a common denominator:
1/5 = 4/20, so:
4/20 - 3/20 = 1/20.
The work rate of C is:
Rate of C = 1/20 work/day.
Step 5: Time Taken by C Alone
The time taken by C alone to finish the work is the reciprocal of the work rate:
Time for C = 1 / (Rate of C) = 1 / (1/20) = 20 days.
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Let's start with the practice questions
Example 1: Baba alone can do a piece of work in 10 days. Anshu alone can do it in 15 days. If the total wages for the work is Rs. 50. How much should Baba be paid if they work together for the entire duration of the work?
(a) Rs. 30
(b) Rs. 20
(c) Rs. 50
(d) Rs. 40
Ans. (a)
Solution:
Step 1: Work Rates of Baba and Anshu
Baba can complete the work in 10 days, so his work rate is:
Rate of Baba = 1/10 work/day. Anshu can complete the work in 15 days, so his work rate is:
Rate of Anshu = 1/15 work/day.
Step 2: Combined Work Rate
The combined work rate is:
Combined Rate = 1/10 + 1/15. Finding the common denominator:
1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6 work/day.
Step 3: Total Duration to Complete the Work
Since they complete 1/6 of the work in one day, the total time to finish the work is:
Total time = 1 / (1/6) = 6 days.
Step 4: Work Done by Baba and AnshuIn 6 days:
- Work done by Baba:
6 × (1/10) = 6/10 = 0.6 (60% of the total work). - Work done by Anshu:
6 × (1/15) = 6/15 = 0.4 (40% of the total work).
Step 5: Wages DistributionThe wages are distributed in proportion to the work done:
- Baba's share of the wages:
0.6 × 50 = 30 Rs. - Anshu's share of the wages:
0.4 × 50 = 20 Rs.
Final Answer: Baba should be paid Rs. 30.
Example 2: Pipe A and B running together can fill a cistern in 6 minutes. If B takes 5 minutes more than A to fill the cistern, then the time in A and B will fill the cistern separately what time?
(a) 15 min, 20 min
(b) 15 min, 10 min
(c) 10 min, 15 min
(d) 25 min, 20 min
Ans. (c)
Solution:
Step 1: Work Rates of A and B
Let the time taken by Pipe A alone to fill the cistern be x minutes. Then, the time taken by Pipe B alone to fill the cistern is x + 5 minutes.
The rates of A and B are:
- Rate of A: 1/x (part of the cistern filled per minute).
- Rate of B: 1/(x+5) (part of the cistern filled per minute).
Together, A and B can fill the cistern in 6 minutes:
1/x + 1/(x+5) = 1/6.
Step 2: Solve for x
Taking the least common denominator:
(x + 5 + x) / [x(x + 5)] = 1/6.
Simplify:
(2x + 5) / (x2 + 5x) = 1/6.
Cross-multiply:
6(2x + 5) = x2 + 5x.
Expand and rearrange:
x2 - 7x - 30 = 0.
Step 3: Solve the Quadratic Equation
Factorize x2 - 7x - 30 = 0:
(x - 10)(x + 3) = 0.
Since time cannot be negative, x = 10.
Step 4: Find Time for B
The time for Pipe B is:
x + 5 = 10 + 5 = 15 minutes.
Final Answer: Pipe A takes 10 minutes, and Pipe B takes 15 minutes to fill the cistern separately. The correct option is (c) 10 min, 15 min.
Example 3: Ajay and Vijay together can do a piece of work in 6 days. Ajay alone does it in 10 days. What time does Vijay require to do it alone?
(a) 20 days
(b) 15 days
(c) 25 days
(d) 30 days
Ans. (b)
Solution: Given that Ajay and Vijay together can do a piece of work in 6 days and Ajay alone can do it in 10 days. We need to find the time Vijay requires to do it alone.
Let the work be 60 units (LCM of 6 and 10).
- Ajay's work efficiency = 60/10 = 6 units/day
- Ajay and Vijay's combined work efficiency = 60/6 = 10 units/day
- Therefore, Vijay's work efficiency = 10 - 6 = 4 units/day
Hence, Vijay alone can complete the work in 60/4 = 15 days.
Therefore, the answer is (b) 15 days.
Question for Practice Questions: Time & Work
Try yourself:Ajay and Vijay can do a piece of work in 28 days. With the help of Manoj, they can finish it in 21 days. How long will Manoj take to finish the work all alone?
Explanation
Time Taken by Manoj to Finish the Work
Step 1: Work Rate of Ajay and Vijay Together
Ajay and Vijay can complete the work in 28 days. Their combined work rate is:
Rate of Ajay and Vijay = 1/28 work/day.
Step 2: Work Rate of Ajay, Vijay, and Manoj Together
Ajay, Vijay, and Manoj together can complete the work in 21 days. Their combined work rate is:
Rate of Ajay, Vijay, and Manoj = 1/21 work/day.
Step 3: Work Rate of Manoj
The work rate of Manoj alone is the difference between the combined rate of all three and the rate of Ajay and Vijay:
Rate of Manoj = Rate of Ajay, Vijay, and Manoj - Rate of Ajay and Vijay.
Substitute the values:
Rate of Manoj = 1/21 - 1/28.
Find the common denominator (LCD = 84):
Rate of Manoj = 4/84 - 3/84 = 1/84 work/day.
Step 4: Time Taken by Manoj Alone
The time taken by Manoj to complete the work is the reciprocal of his work rate:
Time for Manoj = 1 / (Rate of Manoj) = 1 / (1/84) = 84 days.
Final Answer: Manoj will take 84 days to finish the work alone.
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Question for Practice Questions: Time & Work
Try yourself:15 men could finish a piece of work in 210 days. But at the end of 100 days, 15 additional men are employed. In how many more days will the work be complete?
Explanation
Time Required to Complete the Work
Step 1: Total Work
Total work is calculated as:
Total Work = Number of men × Number of days.
Total Work = 15 × 210 = 3150 man-days.
Step 2: Work Completed in 100 Days
The work completed by 15 men in 100 days is:
Work Completed = 15 × 100 = 1500 man-days.
Remaining work is:
Remaining Work = 3150 - 1500 = 1650 man-days.
Step 3: Work Rate with 30 Men
After 100 days, 15 additional men are employed, making the total number of men **30**.
The rate of work is:Work Rate = 30 man-days per day.
Step 4: Time to Complete Remaining Work
The time required to complete the remaining work is:
Time = Remaining Work / Work Rate.
Time = 1650 / 30 = 55 days.
Final Answer: The work will be completed in 55 more days.
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Question for Practice Questions: Time & Work
Try yourself:There are two pipes in a tank. Pipe A is for filling the tank and Pipe B is for emptying the tank. If A can fill the tank in 10 hours and B can empty the tank in 15 hours then find how many hours will it take to completely fill a half empty tank?
Explanation
Step 1: Work Rates of Pipes
Pipe A fills the tank in 10 hours, so the rate of Pipe A is:
Rate of A = 1/10 tank/hour.
Pipe B empties the tank in 15 hours, so the rate of Pipe B is:
Rate of B = 1/15 tank/hour.
Step 2: Combined Rate of Both Pipes
The combined rate of both pipes is:
Combined rate = Rate of A - Rate of B = 1/10 - 1/15.
To subtract the fractions, we find the common denominator (LCD = 30):
1/10 = 3/30, 1/15 = 2/30.
Now, subtract:
Combined rate = 3/30 - 2/30 = 1/30 tank/hour.
Step 3: Time to Fill Half the Tank
The tank is half empty, so half of the tank needs to be filled. The time required to fill half the tank is:
Time = (1/2) / (1/30) = 15 hours.
Final Answer: It will take 15 hours to completely fill the half-empty tank.
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Question for Practice Questions: Time & Work
Try yourself:Raju is twice as good as Vijay. Together, they finish the work in 14 days. In how many days can Vijay alone do the same work?
Explanation
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Question for Practice Questions: Time & Work
Try yourself:There are three Taps A, B and C in a tank. They can fill the tank in 10 hrs, 20 hrs and 25 hrs, respectively. At first, all of them are opened simultaneously. Then after 2 hours, tap C is closed and A and B are kept running. After the 4th hour, tap B is also closed. The remaining work is done by Tap A alone. Find the percentage of the work done by Tap A by itself.
Explanation
The capacity of the tank
= LCM(10, 20 and 25) = 100
Efficiency of A = 100/10 = 10
Efficiency of B = 100/20 = 5
Efficiency of C = 100/25 = 4
Tank filled in 2 hours by A, B, and C
= (10 + 5 + 4) × 2 = 38 unit
According to the question,
After 4 hours from the beginning, tap B is also closed
Tank filled in 2 hours by A & B
= (10 + 5) × 2 = 30 unit
Now, tap B is also closed
Remiang capacity of tank = 100 - 38 - 30 = 32 unit
These 32 unit is filled by A alone.
So, the total work done by A
= Work done in (1st 2 hr + next 2 hr + 32 unit)
= 10 × 2 + 10 × 2 + 32 = 72 unit
Percentage of a tank filled by A = (72/100) × 100 = 72%.
Hence, The Required value is 72%.
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Question for Practice Questions: Time & Work
Try yourself:A can do some work in 24 days, B can do it in 32 days and C can do it in 60 days. They start working together. A left after 6 days and B left after working for 8 days. How many more days are required to complete the whole work?
Explanation
In 6 days A would do 25% of the work and in 8 days B would do 25% of the work himself. So, C has to complete 50% of the work by himself. In all C would require 30 days to do 50% of the work. So, he would require 22 more days.
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Medium Level
Almost 70% of questions in CAT are Medium based questions. Though the conceptually seem easier, the trick is to solve the calculations faster & we curated problems for you to help you do problems easier. Try this question by yourself:
Question for Practice Questions: Time & Work
Try yourself:According to a plan, a drilling team had to drill to a depth of 270 metres below the ground level. For the first three days the team drilled as per the plan. However, subsequently finding that their resources were getting underutilised according to the plan, it started to drill 8 metres more than the plan every day. Therefore, a day before the planned date they had drilled to a depth of 280 metres. How many metres of drilling was the plan for each day.
Explanation
Let n be the number of metres planned per day. Start from the options to find the number of planned days. In the options the 2 feasible values are 30 metres and 27 metres (as these divide 270).
Suppose we check for 30 metres per day, the work would have got completed in 9 days as per the original plan. In the new scenario: 3n + 5(n + 8) = 280 -> n = 30 too. Hence, this option is correct.
Note that if we tried with 27 metres per day the final equation would not match as we would get: 3n + 6(n + 8) = 280 -> which does not give us the value of n as 27 and hence this option is rejected.
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Let's start with the practice questions
Directions for Examples 1 to 3. Read the following and answer the questions that follow.
A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y ) fills 3/8 of the tank in 3 minutes. The third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes.
Example 1: How many minutes will it take to fill the tank if all the 23 pipes are opened at the same time?
(a) 5 minutes
(b) 5 5/ 7 minutes
(c) 6 minutes
(d) 6 5 /7 minutes
Ans: (b)
Solution:
Step 1: Determine the Rate of Each Pipe
Assume each pipe can fill the tank in 130 minutes. The rate of one pipe is:
Rate of one pipe = 1/130 tank/min.
Step 2: Find the Combined Rate of All 23 Pipes
The combined rate of 23 pipes is:
Combined rate = 23 × (1/130) = 23/130 tank/min.
Step 3: Calculate the Time to Fill the Tank
The time required to fill the tank is:
Time = 1 / (Combined rate).
Substitute the combined rate:
Time = 1 / (23/130) = 130/23 minutes.
Simplify:
Time = 5 15/23 minutes.
Final Answer: The time required to fill the tank is approximately 5 5/7 minutes.
The correct option is (b) 5 5/7 minutes.
Question for Practice Questions: Time & Work
Try yourself:A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :
Explanation
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
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Example 2: If the tank is half full and set X and set Y are closed, how many minutes will it take for set Z to empty the tank if alternate taps of set Z are closed.
(a) 12 minutes
(b) 20 minutes
(c) 40 minutes
(d) 16 minutes
Ans. (b)
Solution: Again if we close 4 taps of set Z, the rate of emptying by set Z would be 2.5% per minute.
►A half-filled tank would contain 50% of the capacity and hence, would take 50/2.5 = 20 minutes to empty.
Example 3: A tank holds 100 gallons of water. Its inlet is 7 inches in diameter and fills the tank at 5 gallons/min. The outlet of the tank is twice the diameter of the inlet. How many minutes will it take to empty the tank if the inlet is shut off when the tank is full and the outlet is opened? (Hint: Rate of filling or emptying is directly proportional to the diameter)
(a) 7.14 min
(b) 10.0 min
(c) 0.7 min
(d) 5.0 min
Ans. (b)
Solution:
Step 1: Understand the Given Data
- Tank capacity: 100 gallons.
- Inlet diameter: 7 inches.
- Filling rate via inlet: 5 gallons/min.
- Outlet diameter: Twice the inlet diameter, so:
Outlet diameter = 2 × 7 = 14 inches.
- Rate proportionality: The filling or emptying rate is directly proportional to the diameter of the pipe.
Step 2: Determine the Outlet Rate
Since the outlet diameter is twice the inlet diameter, the outlet rate will be:
Outlet rate = 2 × Inlet rate.
Substitute the inlet rate:
Outlet rate = 2 × 5 = 10 gallons/min.
Step 3: Time to Empty the Tank
The tank holds 100 gallons, and the outlet empties the tank at a rate of 10 gallons/min. The time required to empty the tank is:
Time = Tank capacity / Outlet rate = 100 / 10 = 10 minutes.
Final Answer: The tank will take 10.0 minutes to empty.
The correct option is (b) 10.0 min.
Question for Practice Questions: Time & Work
Try yourself:X takes 4 days to complete one-third of a job, Y takes 3 days to complete one-sixth of the same work and Z takes 5 days to complete half the job. If all of them work together for 3 days and X and Z quit, how long will it take for Y to complete the remaining work done.
Explanation
In three days, the work done will be 25 + 16.66 + 30 = 71.66%. The remaining work will get done by Y in 28.33/5.55 = 5.1 days. [Note: You need to be fluent with your fraction to percentage conversions in order to do well at these kinds of calculations.]
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Question for Practice Questions: Time & Work
Try yourself:Two typists of varying skills can do a job in 6 minutes if they work together. If the first typist typed alone for 4 minutes and then the second typist typed alone for 6 minutes, they would be left with 1/5 of the whole work. How many minutes would it take the slower typist to complete the typing job working alone?
Explanation
Since the first typist types for 4 minutes and the second typist types for exactly 6 minutes, the work left (which is given as 1/5 of the total work) would be the work the first typist can do in 2 minutes.
Thus, the time taken by the first typist to do the work would be 10 minutes and his rate of work would be 10% per minute. Also, since both the typists can do the work together in 6 minutes, their combined rate of work would be 100/6 = 16.66% per minute.
Thus, the second typist’s rate of work would be 16.66 – 10 = 6.66% per minute.
He would take 100/6.66 = 15 minutes to complete the task alone.
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Question for Practice Questions: Time & Work
Try yourself:Each of A, B and C need a certain unique time to do a certain work. C needs 1 hour less than A to complete the work. Working together, they require 30 minutes to complete 50% of the job. The work also gets completed if A and B start working together and A leaves after 1 hour and B works for a further 3 hours. How much work does C do per hour?
Explanation
0.5(A + B + C) = 50% of the work. Means A, B and C can do the full work in 1 hour. Thus, (A + B + C) = 100% From this point it is better to solve through options. Option (c) gives the correct answer based on the following thought process. If c = 50% work per hour, it means C takes 2 hours to complete the work.
Consequently, A would take 3 hours and hence do 33.33% work per hour. Since, A + B + C = 100%, this gives us B’s hourly work rate = 16.66%. For this option to be correct these nos. should match the second instance and the information given there. According to the second condition: A + 4B should be equal to 100%. Putting A = 33.33% and B = 16.66% we see that the condition is satisfied. Hence, this option is correct.
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Question for Practice Questions: Time & Work
Try yourself:Three diggers dug a ditch of 324 m deep in six days working simultaneously. During one shift, the third digger digs as many metres more than the second as the second digs more than the first. The third digger’s work in 10 days is equal to the first digger’s work in 14 days. How many metres does the first digger dig per shift?
Explanation
The per day digging of all three combined is 54 metres. Hence, their average should be 18. This means that the first should be 18 – x, the second, 18 & the third 18 + x.
The required conditions are met if we take the values as 15, 18 and 21 metres for the first, second and third diggers, respectively.
Hence, (a) is the correct answer
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Question for Practice Questions: Time & Work
Try yourself:Two inlet pipes can separately fill a tank in 20 minutes and 15 minutes respectively and a waste pipe can empty the completely filled tank in 12 minutes. On a certain day, the two inlet pipes are turned on simultaneously to fill the empty tank. But after 9 minutes it was found that the waste pipe was also left opened, it was closed immediately. How much more time is required to fill the tank completely?
Explanation
Let total work be 60 units. 1st tap fills 3units per minute, 2nd tap fills 4 units per minute and waste pipe empties 5 units per minute. So, when opened together all three will fill (3 + 4 – 5) = 2 units per min.
Hence in first 9 min, 18 units of tank is filled. Since the waste pipe is closed
∴ The remaining 42 units will require 42 /3 +4 = 6 min to fill.
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Question for Practice Questions: Time & Work
Try yourself:In a factory's total daily wages of 20 men, 30 women and 36 children is Rs. 78. The ratio of work done by a man, a woman and a child in a day is 3 : 2 : 1 respectively. What will be the total wages of 15 men, 21 women and 30 children for 18 weeks?
Explanation
Let the work done by a man, a woman and a child in a day be m, w and c respectively. Then, m = 3c and w = 2c ∴ 20m + 30w + 36c = 60c + 60c + 36c = 156c
Total units of work done in second case = (15m + 21w + 30c) × 7 × 18 = (45c + 42c + 30c) × 7 × 18 = 117c × 7 × 18
Hence, the required total ways 78 /156c = × 117c × 7 × 18 = Rs. 7,371.
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Hard Level
Around 25% of these types of questions come in CAT - If your target is above 95%ile, we recommend you solve these questions.
Example 1: Abbot can do some work in 10 days, Bill can do it in 20 days and Clinton can do it in 40 days. They start working in turns with Abbot starting to work on the first day followed by Bill on the second day and by Clinton on the third day and again by Abbot on the fourth day and so on till the work is completed fully. Find the time taken to complete the work fully?
(a) 16 days
(b) 15 days
(c) 17 days
(d) 16.5 days
Ans. (d)
Solution:
►The work rate would be 10% on the first day, 5% on the second day, and 2.5% on the third day.
►For every block of 3 days, there would be 17.5% of work done.
►In 15 days, the work completed would be 17.5 * 5 = 87.5%.
►On the sixteenth day, work is done = 10% so 2.5% work would be left after 16 days.
►On the 17th day, the rate of work would be 5% and hence it would take half of the 17th day to complete the work.
Thus, it would take 16.5 daysto finish the work in this fashion.
Example 2: A, B, and C working together completed a job in 10 days. However, C only worked for the first three days when 37/100 of the job was done. Also, the work done by A in 5 days is equal to the work done by B in 4 days. How many days would be required by the fastest worker to complete the entire work?
(a) 20 days
(b) 25 days
(c) 30 days
(d) 40 days
Ans. (a)
Solution: The equations are: 3(A + B + C) = 37/100 = 37% of the work. 7(A + B) = 63/10 ; A + B = 9/100 = 9% (Where A, B and C are 1 day’s work of the three respectively).
►Further, 5A = 4B gives us A = 4% and B = 5% work per day.
►In 3 days (A + B + C) do 37% of the work.
►Out of this A and B would do 27% (= 3*9%) of the work.
►So, C would do 3.33% of the work per day. 37- 27/ 3 - Thus, B is the fastest and he would require 20 days to complete the work.
[Question: 1842446]
Question for Practice Questions: Time & Work
Try yourself:Ajit can do as much work in 2 days as Baljit can do in 3 days and Baljit can do as much in 4 days as Diljit in 5 days. A piece of work takes 20 days if all work together. How long would Baljit take to do all the work by himself?
Explanation
Let Ajit’s rate of work be 100/2 = 50 work units per day. Baljit would do 100/3 = 33.33 work units per day and Diljit does 133.33/5 = 26.66 units of work per day.
Their 1 days work = 50 + 33.33 + 26.66 = 110 units of work per day.
In 20 days, the total work done would be 2200 units of work and hence for Baljit to do it alone it would take: 2200/33.33 = 66 days to complete the same work
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Question for Practice Questions: Time & Work
Try yourself:It takes six days for three women and two men working together to complete a work. Three men would do the same work five days sooner than nine women. How many times does the output of a man exceed that of a woman?
Explanation
Solve this using options.
If we check for option (c), i.e., the work of a man exceeds the work of a woman by 5 times, we would get the following thought process: Total work = 6 days * (3 women + 2 men) = 18 woman days + 12 man days = 18 woman days + 60 woman days = 78 woman days.
Thus, 9 women would take 78/9 days = 8.66 days and hence 3 men should do the same work in 3.66 days.
This translates to 3* 3.66 = 10 man days or 50 woman days which is incorrect as the number of woman days should have been 78. Thus, we can reject this option.
If we check for option (d), i.e., the work of a man exceeds the work of a woman by 6 times, we would get the following thought process: Total work = 6 days * (3 women + 2 men) = 18 woman days + 12 man days = 18 woman days + 72 woman days = 90 woman days.
Thus, 9 women would take 90/9 days = 10 days and hence 3 men should do the same work in 5 days.
This translates to 3 * 5 = 15 man days or 90 woman days which is correct as the number of woman days should be 90.
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Question for Practice Questions: Time & Work
Try yourself:In a tank there are four outlets A, B, C and D. These outlets can empty the tank in 10 minutes, 12 minutes, 15 minutes and 18 minutes respectively. If the tank is full and all the outlets are opened how much time will it take to empty the whole tank, if the outlets A and B are closed after 1 minute and 2 minutes respectively, and outlet C is closed 5 minutes before the tank gets empty.
Explanation
Let the capacity of the tank be 180 units. (LCM of 10, 12, 15 and 18) Amount of water drawn in one minute by Outlet Pipe A = 18 Units
Outlet Pipe B = 15 Units Outlet Pipe C = 12 Units
Outlet Pipe D = 10 Units
Let the total time taken to empty the tank with the given conditions be ‘t’ minutes. Amount drawn by A = 1 × 18 = 18 units
Amount drawn by B = 2 × 15 = 30 units
Amount drawn by C = (t–5) × 12 = (12t – 60) units
Amount drawn by D = t × 10 = 10t units
⇒ 18 + 30 + 12t – 60 + 10t = 180 22t = 192 or
t = 96 /11 minutes
=
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