Aptitude :: Time And WorkPage 2
9.  A and B can do a piece of work in 4 and 6 days respectively. If B works on the first day and they work on alternate days, in how many days will twice the amount of work be completed?  (a)29/3 days  (b)10 days  (c)46/5 days  (d)19/2 days 

Answer is: AA and B can do (1/4)th and (1/6)th of the total work in one day.
In 2 days they can do (1/4 + 1/6) = (5/12)th of the total work
In 8 days they can do (20/12)th of the total work
on 9th day B does (1/6)th or (2/12)th of the total work.
on 10th day 2  20/12  2/12 = (2/12)th of the total work is left, which is done by A in (2/3)rd of day.
In 29/3 days twice the amount of work is done.
10.  If P produce 60 cakes in 9 days and Q produce 70 cakes in 21 days, how many days do they take to produce 100 cakes together?  (a)8 days  (b)9 days  (c)10 days  (d)11 days 

Answer is: CNumber of cakes P produces in 1 day = 60/9 = 20/3 cakes.
Number of cakes Q produces in 1 day = 70/21 = 10/3 cakes.
Number of cakes produced by P and Q together In 1 day is (10/3 + 20/3) = 10 cakes.
Number of days to produce 100 cakes is 100/10 = 10 days.
11.  P, Q and R take 7, 12 and 14 days respectively to complete a job, working individually. With the help of S, P, Q and R together complete the work in 2 days. Find S' s share in a total of Rs 4200 paid to them.  (a)Rs. 600  (b)Rs. 1700  (c)Rs. 1200  (d)Rs. 700 

Answer is: BIn 2 days P, Q and R can do (2/7 + 2/12 + 2/14) = (24 + 14 12)/84 = (50/84)th amount of work.
S does (1  50/84) i.e. (34/84)th work.
His share is (34/84) X 4200 = Rs. 1700
12.  P, Q, R and S, working together produce a total of 200 books. In producing books, P is thrice as efficient as Q but 75% less efficient than R. R is half as efficient as S produces. How many books did Q produce?  (a)5  (b)15  (c)10  (d)20 

Answer is: ALet P, Q, R, S produce p, q, r and s books respectively.
so, Given that
P = 3Q â†’ (1)
4Q = R â†’ (2)
2R = S â†’ (3)
P + Q + R + S = 200
3Q + Q + 12Q + 24Q = 200
40Q = 200
Q = 5.
13.  Machine A can do a work in 20 days. An advanced machine B is 25% more efficient than A. In how many days can they complete the work, if they work together?  (a)61/9 days  (b)73/9 days  (c)80/9 days  (d)82/9 days 

Answer is: CIf machine A can do x units of work in 1 day, machine B can do 1.25x units of work in 1 day.
Both working together can do 2.25x units of work in 1 day.
The total work they have to do is (20) X (x) = 20x work.
It is done by both A and B working together in =20x/2.25x = 80/9 days.
14.  A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in:  (a)8 days  (b)10 days  (c)12 days  (d)15 days 

Answer is: C(A + B)'s 1 day's work = (1/15 + 1/10) = 1/6.
Work done by A and B in 2 days = (1/6) X 2 = 1/3.
Remaining work = 1  1/3 = 2/3.
Now,1/15 work is done by A in 1 day.
2/3 work will be done by A in = 15 X 2/3 = 10 days.
Hence, the total time taken = (10 + 2) = 12 days.
15.  A can complete a piece of work in 12 days. A starts the work, work 4 days and quit. B and C take over and complete the remaining work in 12 days. If B can complete half of the work in 12 days, find the time taken by C alone to complete the work?  (a)54 days  (b)60 days  (c)80 days  (d)72 days 

Answer is: DA can do 1/12th of the work in 1 day.
So, A does 1/3rd of the work in 4 days.
B does 1/24th of the working in 4 days.
In 12 days he can complete 1/2 of the work.
So, the amount of work left for C to complete in 12 days = 1  1/2  1/3 = 1/6
C can do the work alone in 12 X 6 = 72 days.
16.  A can complete a certain work in 8 days. A and B work for 2 days and then A leaves and C joins B and both work together and complete the remaining work in 4 days. In how many days can B alone complete the work, if C alone can complete the work in 16 days?  (a)16 days  (b)12 days  (c)20 days  (d)24 days 

Answer is: BA works for 2 days therefore, he completes (2/8)th or (1/4)th of the job.
C works for 4 days and completes (4/16)th or (1/4)th of the job.
So, the rest (1/2) of the job is done by B in 6 days.
B alone can complete the job in 12 days.
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