Time and Work Questions with Answers - Quant PDF Download

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.

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: The ratio of the wages will be the inverse of the ratio of the number of days required by each to do the work.
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 

Ans: (c)

Solution: A + B = 16.66%. From here solve this one using the options.
► 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 

Ans: (a)

Solution: A + M = 8.33, M + B = 6.66 and A = 2B
► 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.

Medium Level

Almost 70% of questions in CAT are of Medium based questions. Though the conceptually they seem easier, trick is to solve the calculations faster & we curated problems for you to help you do problems easier.

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: If all the 23 pipes are opened the per minute rate will be: 10 + 12.5 – 5 = 17.5%
► Option (b) is correct

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: The outlet pipe will empty the tank at a rate which is double the rate of filling (Hence, 10 gallons per minute).
► If the inlet is shut off, the tank will get emptied of 100 gallons of water in ten minutes.

Hard Level

Around 25% of these type 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% work done.
► In 15 days, the work completed would be 17.5 * 5 = 87.5%.
► On the sixteenth day, work 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.