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**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:

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?

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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 **

Hence, the correct answer will be 3:2 for 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 **

► Option (c) fits the situation as it gives us A’s work = 10%, B’s work = 6.66% as also that B takes 5 minutes more than A (as stipulated in the problem).

**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 **

► So, A’s 1 days work = 3.33%, M’s = 5% and B’s = 1.66%.

► Thus, Mohan would require 100/5 = 20 days to complete the work if he works alone.

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?

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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?

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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?

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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?

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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.

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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?

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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:

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.

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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**

If all the 23 pipes are opened the per minute rate will be:

► 10 + 12.5 – 5 = 17.5%

► Option (b) is correct.

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 :

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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**

► 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**

► If the inlet is shut off, the tank will get emptied of 100 gallons of water in

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.

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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?

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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?

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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?

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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?

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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?

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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**

► 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% 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 days **to 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.

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?

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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?

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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.

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