Maths (Time & Work)

#TIME & WORK (SSC,BANK,GENERAL COMPETITIONS)#
EXPLANATIONS & ANSWERS HAVE BEEN ALSO PROVIDED
1. P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?

A. 8/15

B. 7/15

C. 11/15

D. 2/11



Answer : Option A

Explanation :

Amount of work P can do in 1 day = 1/15

Amount of work Q can do in 1 day = 1/20

Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60

Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15

Fraction of work left = 1 – 7/15= 8/15



2. P can lay railway track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they completes the job in 4 days. How much days does it take for R alone to complete the work?

A. 9(3/5) days

B. 9(1/5) days

C. 9(2/5) days

D. 10 days

Answer : Option A

Explanation :

Amount of work P can do in 1 day = 1/16

Amount of work Q can do in 1 day = 1/12

Amount of work P, Q and R can together do in 1 day = 1/4

Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48

=> Hence R can do the job on 48/5 days = 9 (3/5) days



3. P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?

A. 10 days

B. 14 days

C. 15 days

D. 9 days



Answer : Option C

Explanation :

Amount of work P can do in 1 day = 1/20

Amount of work Q can do in 1 day = 1/30

Amount of work R can do in 1 day = 1/60

P is working alone and every third day Q and R is helping him

Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5

So work completed in 15 days = 5 × 1/5 = 1

Ie, the work will be done in 15 days



4. A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in - days if they work together.

A. 18 days

B. 22 ½ days

C. 24 days

D. 26 days



Answer : Option B

Explanation :

If A completes a work in 1 day, B completes the same work in 3 days

Hence, if the difference is 2 days, B can complete the work in 3 days

=> if the difference is 60 days, B can complete the work in 90 days

=> Amount of work B can do in 1 day= 1/90

Amount of work A can do in 1 day = 3 × (1/90) = 1/30

Amount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45

=> A and B together can do the work in 45/2 days = 22 ½ days



5. A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C?

A. Rs. 380

B. Rs. 600

C. Rs. 420

D. Rs. 400


Answer : Option D

Explanation :

Amount of work A can do in 1 day = 1/6

Amount of work B can do in 1 day = 1/8

Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24

Amount of work A + B + C can do = 1/3

Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24

work A can do in 1 day: work B can do in 1 day: work C can do in 1 day

= 1/6 : 1/8 : 1/24 = 4 : 3 : 1

Amount to be paid to C = 3200 × (1/8) = 400



6. 6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in - days.

A. 4 days

B. 6 days

C. 2 days

D. 8 days



Answer : Option A

Explanation :

Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b

Work done by 6 men and 8 women in 1 day = 1/10

=> 6m + 8b = 1/10

=> 60m + 80b = 1 --- (1)

Work done by 26 men and 48 women in 1 day = 1/2

=> 26m + 48b = ½

=> 52m + 96b = 1--- (2)

Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200

Work done by 15 men and 20 women in 1 day

= 15/100 + 20/200 =1/4

=> Time taken by 15 men and 20 women in doing the work = 4 days



7. A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. B alone can complete the work in --- hours.

A. 12 hours

B. 6 hours

C. 8 hours

D. 10 hours



Answer : Option A

Explanation :

Work done by A in 1 hour = 1/4

Work done by B and C in 1 hour = 1/3

Work done by A and C in 1 hour = 1/2

Work done by A,B and C in 1 hour = 1/4+1/3 = 7/12

Work done by B in 1 hour = 7/12 – 1/2 = 1/12 => B alone can complete the work in 12 hours



8. P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. then Q alone can do it in

A. 30 days

B. 25 days

C. 20 days

D. 15 days



Answer : Option B

Explanation :

Work done by P and Q in 1 day = 1/10

Work done by R in 1 day = 1/50

Work done by P, Q and R in 1 day = 1/10 + 1/50 = 6/50

But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as

Work done by P in 1 day × 2 = 6/50

=> Work done by P in 1 day = 3/50

=> Work done by Q and R in 1 day = 3/50

Hence work done by Q in 1 day = 3/50 – 1/50 = 2/50 = 1/25

So Q alone can do the work in 25 days



9. A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?

A. 37 ½ days

B. 22 days

C. 31 days

D. 22 days


Answer : Option A

Explanation :

Work done by A in 20 days = 80/100 = 8/10 = 4/5

Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)

Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)

Work done by A and B in 1 day = 1/15 ---(2)

Work done by B in 1 day = 1/15 – 1/25 = 2/75

=> B can complete the work in 75/2 days = 37 ½ days



10. Machine P can print one lakh books in 8 hours. Machine Q can print the same number of books in 10 hours while machine R can print the same in 12 hours. All the machines started printing at 9 A.M. Machine P is stopped at 11 A.M. and the remaining two machines complete work. Approximately at what time will the printing of one lakh books be completed?

A. 3 pm

B. 2 pm

C. 1:00 pm

D. 11 am



Answer : Option C

Explanation :

Work done by P in 1 hour = 1/8

Work done by Q in 1 hour = 1/10

Work done by R in 1 hour = 1/12

Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120

Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60



From 9 am to 11 am, all the machines were operating.

Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60



Pending work = 1- 37/60 = 23/60

Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11

which is approximately equal to 2



Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm



11. P can finish a work in 18 days. Q can finish the same work in 15 days. Q worked for 10 days and left the job. how many days does P alone need to finish the remaining work?

A. 8

B. 5

C. 4

D. 6



Answer : Option D

Explanation :

Work done by P in 1 day = 1/18

Work done by Q in 1 day = 1/15



Work done by Q in 10 days = 10/15 = 2/3

Remaining work = 1 – 2/3 = 1/3

Number of days in which P can finish the remaining work = (1/3) / (1/18) = 6



12. 3 men and 7 women can complete a work in 10 days . But 4 men and 6 women need 8 days to complete the same work . In how many days will 10 women complete the same work?

A. 50

B. 40

C. 30

D. 20



Answer : Option B

Explanation :

Work done by 4 men and 6 women in 1 day = 1/8

Work done by 3 men and 7 women in 1 day = 1/10

Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as

4m + 6w = 1/8 -(1)

3m + 7w = 1/10 -(2)

Solving equation (1) and (2) , we get m=11/400 and w=1/400

Amount of work 10 women can do in a day = 10 × (1/400) = 1/40

Ie, 10 women can complete the work in 40 days



13. A and B can finish a work 30 days if they work together. They worked together for 20 days and then B left. A finished the remaining work in another 20 days. In how many days A alone can finish the work?

A. 60

B. 50

C. 40

D. 30



Answer : Option A

Explanation :

Amount of work done by A and B in 1 day = 1/30

Amount of work done by A and B in 20 days = 20 × (1/30) = 20/30 = 2/3

Remaining work – 1 – 2/3 = 1/3

A completes 1/3 work in 20 days

Amount of work A can do in 1 day = (1/3)/20 = 1/60

=> A can complete the work in 60 days



14. A can complete a work in 12 days with a working of 8 hours per day. B can complete the same work in 8 days when working 10 hours a day. If A and B work together, working 8 hours a day, the work can be completed in - days.

A. 5 5⁄11

B. 4 5⁄11

C. 6 4⁄11

D. 6 5⁄11



Answer : Option A

Explanation :

A can complete the work in 12 days working 8 hours a day

=> Number of hours A can complete the work = 12×8 = 96 hours

=> Work done by A in 1 hour = 1/96



B can complete the work in 8 days working 10 hours a day

=> Number of hours B can complete the work = 8×10 = 80 hours

=> Work done by B in 1 hour = 1/80



Work done by A and B in 1 hour = 1/96 + 1/80 = 11/480

=> A and B can complete the work in 480/11 hours

A and B works 8 hours a day



Hence total days to complete the work with A and B working together

= (480/11)/ (8) = 60/11 days = 5 5⁄11 days



15. P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work?

A. 9

B. 11

C. 13

D. 15


Answer : Option C

Explanation :

Work done by P in 1 day = 1/23

Let work done by Q in 1 day = q

q × (130/100) = 1/23

=> q = 100/(23×130) = 10/(23×13)

Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13

=> P and Q together can do the work in 13 days
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