CAT 2021: Time & Work | Additional Study Material for CAT PDF Download

Q.1. 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 in 16 months, Anthony and Amar can complete 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

Ans: 32
Let the total work be 48 units. Let Amar do 'm' work, Akbar do 'k' work, and Anthony do 'n' units of work in a month.
Amar and Akbar complete the project in 12 months. Hence, in a month they do 48/12 = 4 units of work.
m + k = 4.
Similarly, k+n = 3, and m+n = 2.
Solving the three equations, we get m = 3/2, k = 5/2, n = 1/2
Here, Amar works neither the fastest not the slowest, and he does 1.5 units of work in a month. Hence, to complete the work, he would take 48/1.5 = 32months.

Q.2. Anu, Vinu and Manu can complete a work alone in 15 days, 12 days and 20 days, respectively. Vinu works everyday. 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
(a) 5
(b) 8
(c) 6
(d) 7

Correct Option is D
Let the total amount of work be 60 units.
Then Anu, Vinu, and Manu do 4, 5, and 3 units of work per day respectively.
On the 1^st day, Anu and Vinu work. Work done on the 1^st day = 9 units
On the 2^nd day, Manu and Vinu work. Work done on the 2^nd day = 8 units
This cycle goes on. And in 6 days, the work completed is 9 + 8 + 9 + 8 + 9 + 8 = 51 units.
On the 7^th day, again Anu and Vinu work and complete the remaining 9 units of work. Thus, the number of days taken is 7 days.

Q.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 ₹ 21000 for the job, then the share of Charu, in INR, proportionate to the work done by him, is
(a) 9000
(b) 9200
(c) 9100
(d) 9150

Correct Option is C
Let Entire work be W
Now Anil worked for 24 days
Bimal worked for 14 days and Charu worked for 14 days .
Now Anil Completes W in 60 days
so in 24 days he completed 0.4W
Bimal completes W in 84 Days
So in 14 Days Bimal completes = W/6
Therefore work done by charu =
Therefore proportion of Charu = 13/30 x 21000 = 9100

Q.4. 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
(a) 11.5
(b) 10
(c) 12.5
(d) 12

Correct Option is B
Let Rahul work at a units/hr and Gautam at b units/hour
Now as per the condition :
8a + 6b =7.5a + 7.5b
so we get 0.5a = 1.5b
or a = 3b
Therefore total work = 8a + 6b = 8a + 2a = 10a
Now Rahul alone takes 10a/10 = 10 hours.

Q.5. Anil can paint a house in 12 days while Barun can paint it in 16 days. Anil, Barun, and Chandu undertake to paint the house for ₹ 24000 and the three of them together complete the painting in 6 days. If Chandu is paid in proportion to the work done by him, then the amount in INR received by him is

Ans: 3000
Now Anil Paints in 12 Days
Barun paints in 16 Days
Now together Arun , Barun and Chandu painted in 6 Days
Now let total work be W
Now each worked for 6 days
So Anil's work = 0.5W
Barun's work = 6W / 16 = 3W/8
Therefore Charu's work =W/2 - 3W/8 = W/8
Therefore proportion of charu = 24000/8 = 3,000