CAT Exam: Time and Work Questions With Solutions | Day 29

Hello aspiring CAT 2022 candidates,
CAT Preparation 2022 in 60 days: On November 27, the CAT exam 2022 for MBA admissions 2023–2025 will take place. In this CAT 2022 60 days preparation guide series of Careers360, we will discuss the strategies for day 29 that can help you prepare well and crack the CAT entrance test 2022.

CAT Preparation 2022 in 60 days

Part-1: CAT 2022 QA Preparation Tips (Quantitative Aptitude)

CAT Exam Important Topic: Time and Work and time and work questions for CAT

Previous Year CAT Questions On Time And Work

Q1. At their usual efficiency levels, A and B together finish a task in 12 days. If A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days. How many days would A take to finish the task if she works alone at her usual efficiency?

1. 18
2. 36
3. 24
4. 12 [CAT exam: 2019]

Time and Work questions for CAT With Solution

Answer: [1]

Let the efficiency of A and B is x and y respectively.

Then, according to the first condition;

Total amount of work = (x+ y) 12

If A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does

Total amount of work = (x/2 + 3y) 9

Both works should be equal,

So, (x+ y) 12= (x/2 + 3y) 9

On solving, x = 2y

Let A will take D days if she works alone;

Total work = xD = (x+ y) 12

Put x = 2y in the above equation;

2y D = (2y + y) 12

On solving, we get D = 18 days.

Q2. When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and finally B works alone to complete the remaining 5% of the job. In how many days can B alone finish the entire job?

1. 16
2. 20
3. 22
4. 18 [CAT exam: 2018]

Time and Work questions for CAT With Solution

Solution: [2]

Since B took 25% more time than B

Let A and B finish a job in 4x and 5x days respectively.

45 % of the work was done by A and B together in 4 days since A did 50% of the work and B did 5% work alone.

Therefore, A and B together can finish the 100% job in 4x 100/45 = 80/9 days.

So,

4x.5x/4x+5x=80/9

On solving, we get x = 4.

So, B alone can finish the job in 20 days.

Part-2: CAT 2022 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)

CAT 2022 Syllabus Topic: Strategy to prepare Problem Solving/Puzzle (Miscellaneous: Jumbled Problems)

CAT previous years questions

Comprehension (RC for CAT):

Eight friends: Ajit, Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and Tapesh are going to Delhi from Kolkata on a flight operated by Cheap Air. In the flight, sitting is arranged in 30 rows, numbered 1 to 30, each consisting of 6 seats, marked by letters A to F from left to right, respectively. Seat A to C is to the left of the aisle (the passage running from the front of the aircraft to the back), and seats D to F are to the right of the aisle. Seats A and F are by the windows and referred to as Window seats, C and D are by the aisle and are referred to as Aisle seats while B and E are referred to as Middle seats. Seats marked by consecutive letters are called consecutive seats (or seats next to each other). A seat number is a combination of the row number, followed by the letter indicating the position in the row; e.g., 1A is the left window seat in the first row, while 12E is the right middle seat in the 12th row.

Cheap Air charges Rs. 1000 extra for any seats in Rows 1, 12 and 13 as those have extra legroom. For Rows 2-10, it charges Rs. 300 extra for Window seats and Rs. 500 extra for Aisle seats. For Rows 11 and 14 to 20, it charges Rs. 200 extra for Window seats and Rs. 400 extra for Aisle seats. All other seats are available at no extra charge.

The following are known:

1. The eight friends were seated in six different rows.
2. They occupied 3 Window seats, 4 Aisle seats and 1 Middle seat.
3. Seven of them had to pay extra amounts, totalling Rs. 4600, for their choices of seats. One of them did not pay any additional amount for his/her choice of seat.
4. Jayanta, Ajit and Byomkesh were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but all of them paid different amounts for their choices of seats. One of these amounts may be zero.
5. Gargi was sitting next to Kikira, and Manik was sitting next to Jayanta.
6. Prodosh and Tapesh were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but they paid different amounts for their choices of the seat. One of these amounts may be zero. [CAT exam: 2017 Slot-2]

Q1. In which row was Manik sitting?

A) 10

B) 11

C) 12

D) 13

Q2. How much extra did Jayanta pay for his choice of the seat?

A) Rs. 300

B) Rs. 400

C) Rs. 500

D) Rs. 1000

Q3. How much extra did Gargi pay for her choice of the seat?

A) 0

B) Rs. 300

C) Rs. 500

D) Rs. 1000

Q4. Who among the following did not pay any extra amount for his/her choice of the seat?

A) Kikira

B) Manik

C) Gargi

D) Tapesh

Solution:

CAT Tip 1: Use the Initial letter for each name

CAT Tip 2: Write Concrete information

1. 8 friends, six different rows, 3 window seats, 4 Aisle seats, 1 middle seat.
2. 7 paid extra amounts of Rs 4600 (Total)
3. J, A, and B are in consecutive rows with increasing numbers paid different amounts in seats marked by the same alphabet. So, the only possibility is rows 10, 11 or 12. All three Aisle or all three windows.
4. P and T were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but they paid different amounts for their choices of the seat. One of these amounts may be zero.
   Possibilities: 1 and 2 or 13 and 14 or 20 and 21. If JAB took window seats, they will take Aisle Seats and vice versa.
5. Gargi was sitting next to Kikira, and Manik was sitting next to Jayanta.

CAT Tip 3: Look for all the possibilities

Case 1: J, A, and B took Window seats

P, and T will take Aisle seats

If J is in the Window seat, then Manik (Row 10) must be in the middle seat.

G, K must be in two Aisle seats

Now, look for extra cost; for window seats of J, A, B = 300 + 200 + 1000 = 1500

For P, T: (Aisle Seats)

There are three Possibilities again

If G and K sit in row either 1 or 13, the extra cost will be Rs 2000. In this case total extra cost will be either less than 4600 or greater than 4600.

If G and K sit in rows other than 1 and 13, maximum extra cost will be Rs 1000; In this case total of extra amount will be less than 4600.

Therefore, this case is not possible.

Case 2: J, A, B took Aisle seats

P, T will take Window seats

If J is in the Aisle seat, then Manik (Row 10) must be in the Aisle seat.

G, K must be in middle seat and window seat (Interchangeable)

Now, look for extra cost; for Aisle seats of J, A, B and M = 500 + 400 + 1000 + 500 = 2400

For P, T: (Window Seats)

There are three Possibilities again

If G and K sit in row either 1 or 13, the extra cost will be Rs 2000. In this case, total extra cost will be equal to 4600 if P and T are in rows 20 and 21.

If G and K sit in rows other than 1 and 13, the extra cost cannot be 4600.

CAT Tip 4: Draw Final Table

Answers:

Q1. (1)

Q2. (3)

Q3. (4)

Q4. (4)

Part-3: CAT Exam Preparation 2022: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)

CAT Exam Important Topic: Reading Comprehension Part-5 (Solving through CAT Previous Years Questions).

CAT Previous Years Question on RC:

Comprehension (RC for CAT):

Read the passage and answer the question based on it.

The end of the age of the internal combustion engine is in sight. There are small signs everywhere: the shift to hybrid vehicles is already under way among manufacturers. Volvo has announced it will make no purely petrol-engined cars after 2019...and Tesla

has just started selling its first electric car aimed squarely at the middle classes: the Tesla 3 sells for $35,000 in the US, and 400,000 people have put down a small, refundable deposit towards one. Several thousand have already taken delivery, and the company hopes to sell half a million more next year. This is a remarkable figure for a machine with a fairly short range and a very limited number of specialised charging stations.

Some of it reflects the remarkable abilities of Elon Musk, the company's founder, as a salesman, engineer, and a man able to get the most out of his factory workers and the governments he deals with... Mr Musk is selling a dream that the world wants to believe in.

This last may be the most important factor in the story. The private car is...a device of immense practical help and economic significance but at the same time a theatre for myths of unattainable self-fulfilment. The one thing you will never see in a car

advertisement is traffic, even though that is the element in which drivers spend their lives. Every single driver in a traffic jam is trying to escape from it, yet it is the inevitable consequence of mass car ownership.

The sleek and swift electric car is at one level merely the most contemporary fantasy of autonomy and power. But it might also disrupt our exterior landscapes nearly as much as the fossil fuel-engine car did in the last century. Electrical cars would of course pollute far less than fossil fuel-driven ones; instead of oil reserves, the rarest materials for batteries would make undeserving despots and their dynasties fantastically rich. Petrol stations would disappear. The air in cities would once more be breathable and their streets as quiet as those of Venice. This isn't an unmixed good. Cars that were as silent as bicycles would still be as dangerous as they are now to anyone they hit without audible warning.

The dream goes further than that. The electric cars of the future will be so thoroughly equipped with sensors and reaction mechanisms that they will never hit anyone. Just as brakes don't let you skid today, the steering wheel of tomorrow will swerve

you away from danger before you have even noticed it...

This is where the fantasy of autonomy comes full circle. The logical outcome of cars which need no driver is that they will become cars which need no owner either. Instead, they will work as taxis do, summoned at will but only for the journeys we actually need. This is the future towards which Uber...is working. The ultimate development of the private car will be to reinvent public transport. Traffic jams will be abolished only when the private car becomes a public utility. What then will happen to our fantasies of independence? We'll all have to take to electrically powered bicycles. [CAT exam: 2017]

Q1. Which of the following statements best reflects the author's argument?

A) Hybrid and electric vehicles signal the end of the age of internal combustion engines.

B) Elon Musk is a remarkably gifted salesman.

C) The private car represents an unattainable myth of independence.

D) The future Uber car will be environmentally friendlier than even the Tesla.

Ans: C

CAT Tips and Tricks: Look for the idea of the passage, and the argument will be related to it.

(B) and (D) are not argumentative statements.

From the last line of the second paragraph to the third paragraph gave your answer.

Q2. The author points out all of the following about electric cars EXCEPT

A) Their reliance on rare materials for batteries will support despotic rule.

B) They will reduce air and noise pollution.

C) They will not decrease the number of traffic jams.

D) They will ultimately undermine rather than further driver autonomy.

Ans: D

CAT Tips and Tricks: Search the statements to eliminate the irrelevant options

Option A: True (4th paragraph)

Option B: True (4th paragraph)

Option C: True (4th paragraph)

Q3. According to the author, the main reason for Tesla's remarkable sales is that

A) In the long run, Tesla is more cost-effective than fossil fuel-driven cars.

B) the US government has announced a tax subsidy for Tesla buyers.

C) the company is rapidly upscaling the number of specialized charging stations for customer convenience.

D) people believe in the autonomy represented by private cars.

Ans: D

CAT Tips and Tricks: Go through options and search in the passage

4th paragraph makes the option D correct.

Q4. The author comes to the conclusion that

A) car drivers will no longer own cars but will have to use public transport.

B) cars will be controlled by technology that is more efficient than car drivers.

C) car drivers dream of autonomy but the future may be public transport.

D) electrically powered bicycles are the only way to achieve autonomy in transportation

Ans: C

Explanation: In the last paragraph, the author says “The logical outcome of cars which need no driver is that they will need no owner either”. This means that they will become public transport.

We will be back with Day 30 tomorrow of the CAT exam preparation guide 2022 for 60 days. Do practice and be focused.