Time and Work – Level 3 (Advanced)

https://youtu.be/uDV4JT66_SI?si=WnD9V8zJI_eoRccJ

1. Anu, Vinu and Manu can complete a work alone in 15 days, 12 days and 20 days, respectively. Vinu works every day. Anu works only on alternate days starting from the first day, while Manu works only on alternate days starting from the second day. Then, the number of days needed to complete the work is  [CAT 2021, Slot 1]

(a) 8

(b) 6

(c) 5

(d) 7

2. Amar, Akbar and Anthony are working on a project. Working together, Amar and Akbar can complete the project in 1 year, Akbar and Anthony can complete it in 16 months, and Anthony and Amar can complete it in 2 years. If the person who is neither the fastest nor the slowest works alone, the time in months he will take to complete the project is  [CAT 2021, Slot 1]

(TITA – enter the numeric answer; no options given)

3. Anil can paint a house in 60 days while Bimal can paint it in 84 days. Anil starts painting and after 10 days, Bimal and Charu join him. Together, they complete the painting in 14 more days. If they are paid a total of ₹21,000 for the job, then the share of Charu, in INR, proportionate to the work done by him, is  [CAT 2021, Slot 2]

(a) 9,100

(b) 9,000

(c) 9,150

(d) 9,200

4. Two pipes A and B are attached to an empty water tank. Pipe A fills the tank while pipe B drains it. If pipe A is opened at 2 pm and pipe B is opened at 3 pm, then the tank becomes full at 10 pm. Instead, if pipe A is opened at 2 pm and pipe B is opened at 4 pm, then the tank becomes full at 6 pm. If pipe B is not opened at all, then the time, in minutes, taken to fill the tank is  [CAT 2021, Slot 2]

(a) 140

(b) 120

(c) 144

(d) 264

5. One day, Rahul started a work at 9 am and Gautam joined him two hours later. They then worked together and completed the work at 5 pm the same day. If both had started at 9 am and worked together, the work would have been completed 30 minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is  [CAT 2021, Slot 3]

(a) 10

(b) 12

(c) 12.5

(d) 11.5

6. A contractor agreed to construct a 6 km road in 200 days. He employed 140 persons for the work. After 60 days, he realized that only 1.5 km of road had been completed. How many additional people would he need to employ in order to finish the work exactly on time?  [CAT 2020, Slot 3]

(TITA – enter the numeric answer; no options given)

7. A work was completed by three persons of equal ability, first one doing m hours for m days, second one doing n hours for n days (m and n being integers) and third one doing 16 hours for 16 days. The work could have been completed in 29 days by third person alone with his respective working hours. If all of them do the work together with their respective working hours, then they can complete it in about

(a) 15

(b) 14

(c) 13

(d) 12

7. A and B do a work in exactly 16 days, B and C do the same work in exactly 12 days while C and A do the same work in about 10 days. If A, B and C can together do the work in integral number of days, then C does the work alone in)

(a) 15

(b) 16

(c) 18

(d) 19

8. Two persons A and B can do a work alone in 29 days. A takes the rest of one day after every 4 days and B takes the rest of one day after every 5 days. If A and B starts working together, then the work will be completed on

(a) 15

(b) 18

(c) 16

(d) 17

9. A contract Is to be completed In 56 days and 104 men were set to work, each working 8 hours a day. After 30 days, 2/5 of the work Is finished. How many additional men may be employed so that work may be completed on time?

(a) 180

(b) 64

(c) 96

(d) 76

Scroll to the bottom for answer key and visit @iimwalabanda YouTube page for video solution

Answer Key

Q.No	Correct Option
Q1	D (7)
Q2	TITA (32)
Q3	A (9,100)
Q4	C (144)
Q5	A (10)
Q6	TITA (40)
Q7	B (16)
Q8	D (17)
Q9	D (76)