# Time & Work

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Directions: Each of the questions given below is followed by series of options among which you have to choose the best one. You can also review your choices by clicking into answer section.

1.  A alone can finish a work in X days. B alone can finish the same work in X+5 days. Together, they take 6 days to complete the work. Find X.

A. 12

B. 8

C. 10

D. 9

Ans: Option C

Explanation:

Part of work completed by A in a day = 1/X

Part of work completed by B in a day = [1/(X+5) (1/X) + (1/(X+5)]

1/6 (2X+5)/(X²+5X) = 1/6 X²+5X

= 6(2X+5) X²-7X-30=0

Solving, X=10

2. A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

A. 12 days

B. 15 days

C. 16 days

D. 18 days

Ans: Option B

Explanation:

A's 2 day's work = 1x (2/20) = 1/10            .

A + B + C.'s 1 day's work = (1/20) + (1/30) + (1/60) = (6/60) = (1/10)

Work done in 3 days = (1/10) +  (1/10) =                (1/5)     .

Now, (1/5) work is done in 3 days.

Whole work will be done in (3 x 5) = 15 days.

3. Twelve men can complete a work in 8 days. Three days after they started the work, 3 more men joined. In many days will all of them together complete the remaining work?

A. 2

B. 5

C. 4

D. 6

Ans: Option C

Explanation:

1 mans 1 days = 1/96

12 men’s 3 days work = (1/8) * 3 = 3/8.

Remaining work 1 — (3/8) = 5/8 15 men 1 day’s work = 15/96

Now, 15/96 work is done by them in 1 day

5/8 work is done by them in (96/15) * (5/8) = 4 days.​

4. If 6 men can make 10 sofas in 2 days, then 8 men can make 8 sofas in

A. 1.8 days

B. 1.5 days

C. 1.2 days

D. 1 day

Ans: Option C

Explanation:  ​

Time is directly proportional to number of sofas inversely proportional to number of people No. of days = (6/8)*(8/10)*2 = 1.2 days

5. A and B can do a job together in 7 days. A is 1 times as efficient as B. The same job can be done by A alone in:

A. 28/3 days

B. 11 days

C. 49/4 days

D. 19/3 days

Ans: Option B

Explanation:

​(A's 1 day's work) : (B's 1 day's work) =  (7/4) : 1   =   7 : 4.

Let A's and B's 1 day's work be 7x and 4x respectively.

Then, 7x + 4x =  1/7

11x = 1/7

x = 1/77               .

A's 1 day's work = (1/77) x 7 = (1/11)

6. A father can do a job as fast as his two sons working together. If one son does the job in 3 hours and the in 6 hours, how many hours does it take the father to do the job?

A. 1

B. 3

C. 2

D. 4

Ans: Option C

Explanation:

Fathers 1 hours work= (1/3) + (1/6) = 1/2

Time taken by father to complete the work = 2 hours.​

7. P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?

A. 60/11

B. 61/11

C. 71/11

D. 72/11

Ans: Option A

Explanation:

P can complete the work in (12 x 8) hrs. = 96 hrs.

Q can complete the work in (8 x 10) hrs. = 80 hrs.

P's1 hour's work =(1/96)  and Q's 1 hour's work =(1/80)                .

(P + Q)'s 1 hour's work =(1/96)  +(1/80) =(11/80)              .

So, both P and Q will finish the work in   (480/11) hrs.

Number of days of 8 hours each = (480/11) x (1/8) = (60/11) days.

8. A and B together can do a piece of work in 12 days, which B and C together can do in 16 days. After A has working at it for 5 days and B for 7 days, C finishes in 13 days. In how many days C alone will do the work?

A. 16

B. 36

C. 24

D. 48

Ans: Option C

Explanation:

​(A + B 5 days work + (B + C  2 days work + Cs 11 days work = 1.

5/12 + 6/12 + Cs 11 days work = 11/24

Cs 1 days work = (11/24) * (1/11) = 1/24

C alone can finish it in 24 days.

9. A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?

A. 23 days

B. 37 days

C. 75/2 days

D. 40 days

Ans: Option C

Explanation:

​Whole work is done by A in (20 x5)/4= 25 days.

Now, [1 –(4/5)i.e., (1/5) work is done by A and B in (3 /5) days.

Whole work will be done by A and B in (3 x 5) = 15 days.

A's 1 day's work =(1/25)                , (A + B 1 day's work) =  (1/15)    .

B's 1 day's work =(1/15)-(1/25) =(4/150)=(2/75)               .

So, B alone would do the work in (75/2)days.

10. Amit can complete a task in 15 hours and Anish can complete the same task in 12 hours. Amit starts the task at 9:00 am and stops working at 2:00pm. Anish starts working on the task at 4:00 pm. At what time is the task completed?

A. 12:00 pm

B. 2:00 am

C. 12:00 am

D. 10:00 pm

Ans: Option C

Explanation:

Amit works for 5 hours. So he completes 5/15 = 1/3 of the task Anish has to complete 2/3rd of the task 12*2/3 = 8 hours are needed. He completes the task at 12:00 am.

11.  A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work?

A. 40

B. 50

C. 54

D. 60

Ans: Option C

Explanation:

(A + B.'s 20 day's work) = (1/30) x 20 =    (2/3)      .

Remaining work = 1 – (2/3) = (1/3)           .

Now, (1/3) work is done by A in 20 days.

Therefore, the whole work will be done by A in (20 x 3) = 60 days.

12. A and B can do a piece of work in 21 and 24 days respectively. They start the work together and after some days, A leaves and B completes the rest of the task in 9 days. After how many days did A leave?

A. 5

B. 6

C. 7

D. 8

Ans: Option C

Explanation:

Part of work completed by A in a day = 1/21

Part of work completed by B in a day = 1/24

Part of work completed by them together in a day = (1/21)+(1/24) = 5/56

Part of work completed by B in 9 days = 9/24 = 3/8

If A left after x days, (5x/56)+(3/8) = 1 x = 7

13. Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

A. 3 : 4

B. 4 : 3

C. 5 : 3

Ans: Option B

Explanation:

(20 x 16) women can complete the work in 1 day.

1 woman's 1 day's work =(1/320)            .

(16 x 15) men can complete the work in 1 day.

1 man's 1 day's work = (1/240)

So, required ratio=(1/240): (1/320)

=(1/3) : (1/4)

= 4 : 3 (cross multiplied).

14. 15 men can build a 500m long wall in 30 days. In how many days can 30 men build a 1.2 km long wall?

A. 48 days

B. 24 days

C. 40 days

D. 36 days

Ans: Option D

Explanation:

No. of days is directly proportional to the length of the wall and inversely proportional to the number of men.

No. of days = (1200/500)*(15/30)*30 = 36 days

15. X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?

A. 40/3 days

B. 15 days

C. 20 days

D. 26 days

Ans: Option A

Explanation:

Work done by X in 8 days = 1x (8/40) =(1/5)         .

Remaining work =1 –(1/5) = (4/5)

Now,(4/5)work is done by Y in 16 days.

Whole work will be done by Y in 16 x (5/4)= 20 days.

X's 1 day's work = (1/40) , Y's 1 day's work = (1/20)          .

(X + Y)'s 1 day's work = (1/40)   + (1/20) = (3/40)               .

Hence, X and Y will together complete the work in (40/3) days.

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