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Five men A, B, C, D and E can do a piece of work in 20, 10, 30, 40 and 50 days respectively. A, B, and C started the work and they work for 2 days after which A and B left the work and D joins the work. D and C work another 3 days together after which C leaves and E joins the work. Find in how many days E and D completed the rest of the work.

Five men A, B, C, D and E can do a piece of work in 20, 10, 30, 40 and 50 days respectively. A, B, and C started the work and they work for 2 days after which A and B left the work and D joins the work. D and C work another 3 days together after which C leaves and E joins the work. Find in how many days E and D completed the rest of the work. Correct Answer 10.2 days

Let the total units of work be 600

 

DAYS TO COMPLETE THE WORK

Per day capacity

A

20

30 units

B

10

60 units

C

30

20 units

D

40

15 units

E

50

12 units

 

A, B, and C started the work and they work for 2 days

⇒ Number of units produced in two days by A, B and C = (30 + 60 + 20) × 2 = 220 units

Then A and B left the work and D and C work another 3 days together

⇒ Number of units produced in 3 days by D and C = (15 + 20) × 3 = 35 × 3 = 105 units

⇒ Work left for D and E = 600 – 220 – 105 = 275 units

∴ D and E will complete rest of the task in 275/(15 + 12) days = 10.2 days

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