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All questions of Time And Work for CLAT Exam

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A factory produces nuts and bolts. A machine in it produces only nuts while another produces only bolts. The machine producing only nuts produces 500 nuts per minute and need to be cleared for 10 minutes after production of 2000 nuts. The machine producing only bolts produces 600 bolts per minute and needs to be cleared for 15 minutes after production of 3000 bolts. Find the minimum time required to produce 6000 pairs of bolts and nuts if both machines are operated simultaneously.
  • a)
    32 minutes
  • b)
    20 minutes
  • c)
    25 minutes
  • d)
    40 minutes
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Preeti Khanna answered
2000 nuts are produced in 14 minutes (10 minutes break and 500 nuts per minutes so 4 minutes to produce 2000 nuts ), for next 2000 nuts it will take 14 minutes more, and for more two thousand it will take 4 minutes more, so total time = 32 minutes
similarly, 6000 bolts are produced in 20 + 5 = 25 minutes
so minimum time required is 32 minutes

A and B together can do a piece of work in 24 days, which B and C together can do it in 32 days. After A has been working at it for 10 days and B for 14 days, C finishes it in 26 days. In how many days C alone will do the work?
  • a)
    32
  • b)
    36
  • c)
    44
  • d)
    48
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?

Anaya Patel answered
Correct Answer :- d
Explanation : Work done by (A+B)'s in 1 day = 24
work done by (B+C)'s in 1 day = 32
Let C does a work in x days
Then work done by C in a day = 1/x
According to the question
A's 10 day's work + B's 14 day's work + C's 26 day's work = 1
10A + 14B + 26C = 1 ;
10A + 10B + 4B + 4C + 22C = 1 ;
10(A + B ) + 4( B + C ) + 22C = 1 ;
10( 1/24 ) + 4( 1/32 ) + 22C = 1 ;
10/24 + 4/32 + 22C = 1 ;
13/24 + 22C = 1 ;
22C = 1 - 13/24 ;
22C = 11/24 ;
2C = 1/24 ;
C = 1/48 ;
Therefore , C alone takes 48 days to finish the job.

A piece of work can be done by 6 men and 5 women in 6 days or 3 men and 4 women in 10 days. It can be done by 9 men and 15 women in how many days ?
  • a)
    3 days
               
  • b)
    4 days
  • c)
    5 days
              
  • d)
    6 days
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Avantika Chakraborty answered
To calculate the answer we need to get 1 man per day work and 1 woman per day work.
Let 1 man 1 day work =x
and 1 woman 1 days work = y. 
=> 6x+5y = 1/6 
and 3x+4y = 1/10 
On solving, we get x = 1/54 and y = 1/90 
(9 men + 15 women)'s 1 days work = 
(9/54) + (15/90) = 1/3 
9 men and 15 women will finish the work in 3 days

If P can do 1/3 of the work in 5 days and Q can do 1/4 of the work in 6 days, then how much money will Q get if they were paid a total of 390 rupee?
  • a)
    120
  • b)
    150
  • c)
    170
  • d)
    190
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Bank Exams India answered
sol = P can alone complete the whole work in 15 days and Q can complete the same work alone in 24 days. So ratio of work done by them 1/15: 1/24 i.e. 8: 5
Q get = (5/13)*390 = 150

A, B and C together earn Rs. 150 per day while A & C together earn Rs. 94 and B and C together earn Rs. 76. The daily earning of C is:
  • a)
    Rs. 75
  • b)
    Rs. 56
  • c)
    Rs. 34
  • d)
    Rs. 20
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?

Sagar Sharma answered
To solve this problem, we can use a system of equations. Let's assign variables to the daily earnings of A, B, and C.

Let A's daily earning be x, B's daily earning be y, and C's daily earning be z.

According to the given information, A, B, and C together earn Rs. 150 per day. So we can write the equation:

x + y + z = 150

We are also given that A + C together earn Rs. 94, so we can write the equation:

x + z = 94

Similarly, B + C together earn Rs. 76, so we can write the equation:

y + z = 76

Now we have a system of three equations with three variables. We can solve this system to find the value of z, which represents C's daily earnings.

We can solve this system by substitution or elimination. Let's use elimination:

First, let's subtract the second equation from the first equation to eliminate z:

(x + y + z) - (x + z) = 150 - 94

Simplifying, we get:

y = 56

Now we have the value of y.

Next, let's subtract the third equation from the first equation to eliminate z:

(x + y + z) - (y + z) = 150 - 76

Simplifying, we get:

x = 74

Now we have the value of x.

Finally, we can substitute the values of x and y into the second equation to solve for z:

74 + z = 94

Subtracting 74 from both sides, we get:

z = 20

Therefore, C's daily earnings are Rs. 20.

Hence, the correct answer is option D) Rs. 20.

A can do a piece of work in 12 hours and with the help of his son, he is able to do it in 8 hours. How many hours will the son alone take to finish the work?
  • a)
    20 hours
  • b)
    24 hours
  • c)
    4 hours
  • d)
    None
  • e)
    All of the above
Correct answer is option 'B'. Can you explain this answer?

Kavya Saxena answered
Correct Answer :- b
Explanation : M can do 1/12 work in a day.
M and S altogether will do 1/8 work in a day.
Work of M in a day + Work of S in a day
1/M + 1/S = 1/8
1/12 + 1/S = 1/8
1/S = 1/8 – 1/12
1/S = 1/24
S = 24
That means S in one day can do 24 work

8 men can do a work in 12 days. After 6 days of work four more men were employed. In how many days would the remaining work be done. 
  • a)
    2 days                      
  • b)
    3 days
  • c)
    4 days                      
  • d)
    5 days
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Kavya Sharma answered
Description for Correct answer:
let 1 men does 1 unit of work per day
Total work: 8x12=96units 
6 days work of 8 men
=8x6=48 units. 
work lelt =96−48=48 units 
After 6 days 4 men join. so total men is 12 men (8+4) they will do 12 unit of work per day 
Now,
remaining work completed in 
=48/12
= 4 days

A does half as much work as B does in one sixth of the time. If together they take 20 days to complete the work, then what is the time taken by A to complete the work independently.
  • a)
    80/3 days
  • b)
    100/3 days
  • c)
    60/3 days
  • d)
    140/3 days
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Faizan Khan answered
Let B complete the work in X days so in one day work done by B is 1/x
as A do half work in one-sixth of the time so A will complete work in 2*x/6 = x/3 days
One day work of A and B i.e. 3/x + 1/x = 1/20. So we get x = 80
So time taken by A alone = 80/3 days

A is thrice as good as workman as B and takes 10 days less to do a piece of work than B takes. B can do the work in
  • a)
    12 days
  • b)
    15 days
  • c)
    20 days
  • d)
    30 days
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Kendrika answered
Ratio of times taken by A and B = 1:3
Means B will take 3 times which A will do in 1 time

If difference of time is 2 days, B takes 3 days
If difference of time is 10 days, B takes (3/2) * 10 =15 days

Mahesh and Umesh can complete a work in 10 days and 15 days respectively. Umesh starts the work and after 5 days Mahesh also joins him. In all, the work would be completed in
  • a)
    7 days
  • b)
    9 days
  • c)
    11 days
  • d)
    12 days
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Naman Agrawal answered
Umesh 5 days work =5/15;
remaining work =1-1/3=2/3;
together 1 day work of Mahesh and Umesh = 1/15+1/10= 1/6;
so, they will do together 2/3 of work in =(2/3)/+(1/6) =4 days.
hence, the work was completed in (4+5) =9 days. op(b)

A and B can together finish a work in 30 days. They worked for it for 20 days and then B left. The remaining work done by A alone in 20 more days. A alone can finish the work in
  • a)
    48 days
  • b)
    50 days
  • c)
    54 days
  • d)
    60 days
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?

Sajal Bdw answered
Amount of work done in 1 day = 1/30
Amount of work done in 20 days = 20 * (1/30) = 2/3 
Remaining work = 1 - 2/3 = 1/3
Given, A completes 1/3 work in 20 days.
Therefore, A can finish the whole work in (20 x 3) = 60 days.
HENCE OPTION D IS THE ANSWER

A and B can do a piece of work in 4 days, B and C in 6 days and A, B and C all together in 3 days, what time will A and C take to do it?
  • a)
    4 days
  • b)
    8 days
  • c)
    12 days
  • d)
    None
  • e)
    All of the above
Correct answer is option 'A'. Can you explain this answer?

Nishtha Pandey answered
(A+B)'s one day work= 1/4
(B+C)'s one day work= 1/6
(A+B+C)'s one day work= 1/3
(A+C)'s one day work=?
now,
(A+B)'s one day work+C's one day work=1/3
1/4+C's one day work=1/3
C's one day work=1/12
A's one day work+(B+C)'s one day work=1/3
A's one day work+1/6=1/3
A's one day work= 1/6
so,
(A+C)'s one day work= 1/12+1/6=3/12=1/4
both together will take 4days to complete the work.

Twelve men can complete a work in 8 days. Three days after they started the work, 3 more men joined them. In how many days will all of them together complete the remaining work:
  • a)
    2
  • b)
    4
  • c)
    5
  • d)
    6
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Chahat Goyal answered
Total work= 12×8 =96
together they work for 3 days, then 3×12=36
remaining work= 96- 36=60
now 3 more men join them, total workers =15
time taken to complete the remaining work=60/15= 4
Hence, correct option is 'B'.

A does half as much work as B in one third of the time taken by B. If together they take 20 days to finish the work then what will be the share of A if 1000 rupees is given for the whole work?
  • a)
    400
  • b)
    500
  • c)
    600
  • d)
    700
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Aarav Sharma answered
Given:
- A does half as much work as B
- A takes one-third of the time taken by B

Let's assume that B takes 'x' days to complete the work. Therefore, A takes '2x' days to complete the work.

Since A and B together take 20 days to finish the work, we can write the equation:

1/x + 1/2x = 1/20

Solving this equation, we get:

2 + 1 = x/20
3 = x/20
x = 60

So, B takes 60 days to complete the work, and A takes 2x = 120 days to complete the work.

Now, to find the share of A if 1000 rupees is given for the whole work:

The share of A is directly proportional to the amount of work done by A.

The amount of work done by A is given by:

Work done by A = (1/2) * Total work

Total work = 1000 rupees

Therefore, the share of A = (1/2) * 1000 = 500 rupees.

Hence, the correct answer is option 'C' - 600.

A and B can do a work in 12 days, B and C in 15 days, C and A in 20 days. A alone can do the work in
  • a)
    60 days                    
  • b)
    30 days
  • c)
    20 days                    
  • d)
    6 days
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Ollivia X answered
A+B 1day work= 1/12. B+C 1day work= 1/15.
C+A 1day work = 1/20.

1 day work of(A+B+C)= (1/12 +1/15+1/20)÷2 = 1/10.

A's 1 day work = 1day work of (A+B+C) - 1day work of (B+C)

= 1/10 - 1/15
= 1/30.

so, A will alone take 30 days yo do the work.

P, Q and R can do a piece of work in 16, 24 and 30 days respectively. They started the work simultaneously but P stops the work after 4 days and Q called off the work 2 days before the completion. In what time the work is finished?
  • a)
    100/9 days
  • b)
    100/11 days
  • c)
    100/7 days
  • d)
    100/13 days
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Aarav Sharma answered
To find the time taken to complete the work, we need to calculate the work done per day by each person.

Let's denote the work done by P, Q, and R per day as Pd, Qd, and Rd respectively.

Given:
P completes the work in 16 days, so Pd = 1/16 (as 1 work is done in 16 days)
Q completes the work in 24 days, so Qd = 1/24 (as 1 work is done in 24 days)
R completes the work in 30 days, so Rd = 1/30 (as 1 work is done in 30 days)

Let's assume the total work to be done is 1 unit.

Work done by P in 4 days = Pd * 4 = (1/16) * 4 = 1/4

Remaining work = 1 - 1/4 = 3/4

Now, Q called off the work 2 days before completion, which means Q worked for (24 - 2) = 22 days.

Work done by Q in 22 days = Qd * 22 = (1/24) * 22 = 11/12

Remaining work = 3/4 - 11/12 = 9/12 - 11/12 = -2/12 = -1/6

The negative value indicates that the work is already completed before Q called off the work.

Since R was working until the completion of the work, R worked for a total of 30 days.

Work done by R in 30 days = Rd * 30 = (1/30) * 30 = 1

Therefore, the work is already completed when Q called off the work.

The remaining work is negative, indicating that the work is already finished.

Hence, the work is finished in 22 days.

Therefore, the correct answer is option A) 100/9 days.

4 men and 6 women can complete 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 the work.
  • a)
    50                            
  • b)
    45
  • c)
    40                            
  • d)
    35
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Prerna Sen answered
Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.
Then, 4x + 6y = 1/8
and 3x + 7y = 1/10
Solving the two equations, we get: x = 11/400, y = 1/400
1 woman's 1 day's work = 1/400
10 women's 1 day's work = (1/400)*10 = 1/40
Hence, 10 women will complete the work in 40 days

A tank is filled by a pipeA in 32 min. and pipe B in 36 min. When filled, it can be emptied by pipe C in 20 minute. If all the three pipes are opened simultaneously 1/3rd of tank will be filled in
  • a)
  • b)
  • c)
  • d)
    None
  • e)
    All of the above
Correct answer is option 'B'. Can you explain this answer?

Nishtha Pandey answered
Part filled by A 1 min=1/32
part filled by B in 1 min=1/36
part emptied by C in 1 min=1/20
Net part filled in 1 min=1/32+1/36-1/20
=13/1440
the tank will be full in=1440/13 min
1/3rd of the tank will be full in=1440×3/13
=480/13
=36 12/13min

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