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Practice Test: Time & Work - 1 - CAT MCQ


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10 Questions MCQ Test - Practice Test: Time & Work - 1

Practice Test: Time & Work - 1 for CAT 2024 is part of CAT preparation. The Practice Test: Time & Work - 1 questions and answers have been prepared according to the CAT exam syllabus.The Practice Test: Time & Work - 1 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Practice Test: Time & Work - 1 below.
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Practice Test: Time & Work - 1 - Question 1

In a stream, Q lies in between P and R such that it is equidistant from both P and R. A boat can go from P to Q and back in 6 hours 30 minutes while it goes from P to R in 9 hours. How long would it take to go from R to P?

Detailed Solution for Practice Test: Time & Work - 1 - Question 1

Since P to R is double the distance of P to Q,
Therefore, it is evident that the time taken from P to R and back would be double the time taken from P to Q and back (i.e. double of 6.5 hours = 13 hours).

Since going from P to R takes 9 hours, coming back from R to P would take 4 hours i.e. 139 = 4

So Option A is correct

Practice Test: Time & Work - 1 - Question 2

A and B together can do a piece of work in 50 days. If A is 40% less efficient than B, in how many days can A working alone complete 60% of the work?

Detailed Solution for Practice Test: Time & Work - 1 - Question 2

Given:

A and B together can do a piece of work in 50 days.

A is 40% less efficient than B

Concept used:

Total work = Efficiency of the workers × time taken by them

Calculation:

Let the efficiency of B be 5a

So, efficiency of A = 5a × 60%

⇒ 3a

So, total efficiency of them = 8a

Total work = 8a × 50

⇒ 400a

Now,

60% of the work = 400a × 60%

⇒ 240a

Now,

Required time = 240a/3a

⇒ 80 days

∴ A can complete 60% of the work working alone in 80 days.

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Practice Test: Time & Work - 1 - Question 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

Detailed Solution for Practice Test: Time & Work - 1 - Question 3

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

Practice Test: Time & Work - 1 - Question 4

Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is

Detailed Solution for Practice Test: Time & Work - 1 - Question 4

Since time taken to finish work is in the ratio 5:8:10

So efficiency will be in the ratio 40/5:40/8:40/10 = 8:5:4

So, Anu does 8 units per hour, Tanu does 5 and Manu does 4.

Total work = 4*8*(8+5+4) = 544

Work done by Anu and Tanu =  6*6.67*(8+5) = 520

Work remaining = 544 – 520 = 24

Time taken by Manu to complete = 24/4 = 6 hours

Practice Test: Time & Work - 1 - Question 5

X can do a piece of work in 20 days. He worked at it for 5 days and then Y finished it in 15 days. In how many days can X and Y together finish the work?

Detailed Solution for Practice Test: Time & Work - 1 - Question 5
  • X’s five day work = 5/20 = 1/4. Remaining work = 1 – 1/4 = 3/4.
  • This work was done by Y in 15 days. Y does 3/4th of the work in 15 days, he will finish the work in 15 × 4/3 = 20 days.  
  • X & Y together would take 1/20 + 1/20 = 2/20 = 1/10 i.e. 10 days to complete the work.

So Option C is correct

Practice Test: Time & Work - 1 - Question 6

Three machines, A, B and C can be used to produce a product. Machine A will take 60 hours to produce a million units. Machine B is twice as fast as Machine A. Machine C will take the same amount of time to produce a million units as A and B running together. How much time will be required to produce a million units if all the three machines are used simultaneously?

Detailed Solution for Practice Test: Time & Work - 1 - Question 6

As machine B's effciency is twice as of A's, Hence, it will complete its work in 30 hours.

And C's effciency is putting A and B together i.e. = 20 hours ((1/60 + 1/30)-1)

Now if all three work together, then it will be completed in x (say) days.

or x = 10 hours

Practice Test: Time & Work - 1 - Question 7

A, B and C individually can finish a work in 6, 8 and 15 hours respectively. They started the work together and after completing the work got Rs.94.60 in all. When they divide the money among themselves, A, B and C will respectively get (in Rs.)

Detailed Solution for Practice Test: Time & Work - 1 - Question 7

Money will be distributed in the ratio of work done in an hour.
i.e. 1/6 : 1/8 : 1/15
or 20:15:8
Hence part of A will be = 20/43 × 94.6 = 44
part of B will be = 15/43 ×  94.6 = 33
part of C will be = 8/43 × 94.6 = 17.60

Practice Test: Time & Work - 1 - Question 8

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

Detailed Solution for Practice Test: Time & Work - 1 - Question 8

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 = 3000

Practice Test: Time & Work - 1 - Question 9

Two pipes, when working one at a time, can fill a cistern in 3 hours and 4 hours, respectively while a third pipe can drain the cistern empty in 8 hours. All the three pipes were opened together when the cistern was 1/12 full. How long did it take for the cistern to be completely full?

Detailed Solution for Practice Test: Time & Work - 1 - Question 9

Let the total amount of work in filling a cistern be 24 units. (LCM of 3, 4 and 8)

Work done by pipe 1 in 1 hour = 24/3 = 8 units.

Work done by pipe 2 in 1 hour = 24/4 = 6 units.

Work done by pipe 3 in 1 hour = 24/ (-8) = -3 units

Total work done in 1 hour = 8 + 6 – 3 = 11 units

The time required to complete 11/12th of the work = 11/12 × 24/ 11 = 2 hours

∴ The correct answer is 2 hours.

Practice Test: Time & Work - 1 - Question 10

A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe lls the empty tank in 8 hours. If the outlet pipe is open then the inlet pipe lls the empty tank in 10 hours. If only the outlet pipe is open then in how many hours the full tank becomes half-full?

Detailed Solution for Practice Test: Time & Work - 1 - Question 10

Let the time taken by the outlet pipe to empty = x hours
Then,

=> x+ 40
Hence time taken by the outlet pipe to make the tank half-full = 40/2 = 20 hour

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