Directions : Study the following information carefully and answer the questions given beside.
 
Five persons A, B, C, D and E were employed to complete a piece of work. 
 
⇒ All the five persons A, B, C, D and E worked for different number of days, i.e. 5, 4, 4, 4 and ‘n’ days respectively. 
 
⇒ The percentage of work done by A, B, C and E is 25%, 20%, 10% and 20% respectively and the remaining percentage of work is done by D.
 
1
 In how many days, A and D will do the whole work?
» Explain it
A
A does 25% of work in 5 days, 100% work will be done in 20 days

D does [100 – (25 + 20 + 10 + 20)] = 25% of work in 4 days, 100% work will be done in 16 days

Total work = LCM (20, 16) = 80 units

A does =  80  = 4 units/day
20

D does =  80  = 5 units/day
16

A + D = 4 + 5 = 9 units/day

So, total work will be done in =  80  days
9

Hence, option A is correct.
2
B and E together do the work in 100/11 days. In how many days E can do the whole work alone?
» Explain it
B
B does 20% work in 4 days then, 100% will be done in 20 days.

Let the total amount of work be 100 units.

B does 5 units/day.

B + E =  100  units/day = 11 units/day
100/11

E does (11 – 5) = 6 units/day

The reqd. answer =  100  =  50  days
6 3

Hence, option B is correct.
3
A & B, B & C, C & D do the work in the given combination and order as given respectively and the cycle repeats, then in how many days 40% work will be done?
» Explain it
C
A’s efficiency 20 days to do whole work 
 
B’s efficiency 20 days to do whole work 
 
C’s efficiency 40 days to do whole work 
 
D’s efficiency 16 days to do whole work 
 
Total units of work = LCM(20, 20, 40, 16) = 80 units 
 
A = 4 units/day 
 
B = 4 units/day 
 
C = 2 units/day 
 
D = 5 units/day 
 
40% of whole work is = 80 × 0.4 = 32 units 
 
A + B = 4 + 4 = 8 units/day 
 
B + C = 4 + 2 = 6 units/day 
 
C + D = 2 + 5 = 7 units/day 
 
Now left amount of target work after 3 days = 32 – (8 + 6 + 7) = 11 units 
 
4th day work done = A + B = 8, so left = 11 – 8 = 3
 
So the next 3 units will be done by B and C together in haf day only.
 
The required answer is = 4.5 days
 
Hence, option C is correct.
4
20% of the work was done by A and B, then 50% of the left work was done by D and at last the rest of work was done by B and C. Find the number of total days taken to do the whole work.
» Explain it
C
A, B, C and D separately can do the work in 20, 20, 40 and 16 days respectively.

Total work = LCM (20, 20, 40, 16) = 320 units [ For ease of calculation 320 is taken as LCM and not 80]

A = 16 units/day

B = 16 units/day

C = 8 units/day

D = 20 units/day

A + B = 16 + 16 = 32 units/day

B + C = 16 + 8 = 24 units/day

20% work will be done in

(320 × 20/100)  = 2 days (by A and B)
32

50% of the left work will be done in

320 – 64  =  128  = 6.4 days (by D)
2 20

Rest is done =  128  = 5.33 days (by B and C)
24

The answer is = 2 + 6.4 + 5.33 = 13.73 days

Hence, option C is correct.
5
F alone takes 15 more days than A alone to complete the whole work. If F works with 50% more efficiency, then in how many days he can do the whole work alone?
» Explain it
D
A needs 20 days to do whole work

∴ F will take 35 days to do the whole job.

With 150% of his efficiency =  35 × 100  =  70  days
150 3

Hence, option D is correct.