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## CAT 2022 : Time and Work Practice Exercise-3

CAT Quantitative Aptitude section consists of problems based on Time and Work which have a considerate amount of weightage. The problems are based on amount of work done by people and the respective time taken by them. Cumulative work or total time taken is given and you are asked the independent time taken and vice versa. In this post, we share CAT Time and Work Problems and Solutions that you can use to super-charge your preparation and have a taste of the problems asked for this area.

Question 1: If 10 men or 20 boys can make 260 mats in 20 days, then 8 men and 4 boys will make how many mats?
(1) 260
(2) 240
(3) 280
(4) 520

### Answer and Explanation

10 men = 20 boys

∴ 1 man = 2 boys

∴ 8 men + 4 boys

= (16 + 4) boys = 20 boys

Hence, 8 men and 5 boys will make 260 mates in 20 days.

Question 2: 20 men or 24 women can com¬plete a piece of work in 20 days. If 30 men and 12 women under-take to complete the work how much time will they take?
(1) 10 days
(2) 12 days
(3) 15 days
(4) 16 days

### Answer and Explanation

20 men ≡ 24 women

⇒ 5 men ≡ 6 women

∴ 30 men + 12 women = 30 men+10 men=40 Men

∴ M1D1 = M2D2

⇒ 20 Men× 20 Days = 40 Men × D2days

⇒ D2 = (20 x 20)/40 = 10 days

Question 3: 8 days are taken by one man and one woman together to complete the job. A man alone can complete the work in 10 days. In how many days can one woman alone complete the work?
(1) 140/9
(2) 30
(3) 40
(4) 42

### Answer and Explanation

Work done by 1 woman in 1 day

= 1/8 – 1/10 = (5-4)/40 = 1/40

∴ One woman will complete the wok in 40 days.

Question 4: 4 men and 6 women can com¬plete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

(1) 50
(2) 45
(3) 40
(3) 35

### Answer and Explanation

Let 1 man’s 1 day’s work = x and

1 woman’s 1 day’s work = y

Then, 4a + 6b = 1/8

3a + 7b = 1/10

On solving, we get b = 1/400

∴ 10 women’s 1 day’s work

= 10/400 = 1/40

∴ 10 women will finish the work in 40 days.

Question 5: A man, a woman and a boy can complete a work in 20 days, 30 days and 60 days respectively. How many boys must assist 2 men and 8 women so as to com¬plete the work in 2 days?
(1) 8
(2) 12
(3) 4
(4) 6

### Answer and Explanation

Extra tips for CAT Time and Work Problems and Solutions:
• You can brush up the basic to solve Time and work problems by going through your 11th and 12th text books as well as school textbooks. This topic is relatively easy and needs basic knowledge of arithmetic and a basic understanding of the relationship between time and work.
• The most important formula you need to remember for solving every time and work formula is:
If X can do some piece of work in say ‘n’ number of days, then X’s 1 day’s work is equal to 1/n.
• You must always remember that Time and work are inversely proportional to each other.
• Solve as many time and work problems as possible. Some of the problems can be solved by simple logic and do not need any solving.
• Time and Work problems are less time consuming and definitely worth attempting in the exam.

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