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Select the correct alternative from the given choices. A, B and C can finish certain piece of work in 12 days, 15 days and 20 days respectively. A started working and is assisted by B and C on alternative days. This way, A, B and C finishes 85% of the total work. The remaining work is finished by D and the total number of days taken to finish the work is 9 days. Find the number of days C and D will take to finish half of this work when C works at 75% of his efficiency?

Select the correct alternative from the given choices. A, B and C can finish certain piece of work in 12 days, 15 days and 20 days respectively. A started working and is assisted by B and C on alternative days. This way, A, B and C finishes 85% of the total work. The remaining work is finished by D and the total number of days taken to finish the work is 9 days. Find the number of days C and D will take to finish half of this work when C works at 75% of his efficiency? Correct Answer 40 / 7

Let the total work be 60(LCM of 12, 15 and 20)

The amount of work A, B and C do in a day is 5, 4 and 3 units respectively.

⇒ A and B do 9 units of work in a day.

⇒ A and C do 8 units of work in a day.

Thus, 17 units of work is completed in two days.

⇒ 85% of the total work = (85 / 100) × 60 = 51

51 units of work will be completed in 3 × 2 = 6 days

Hence, D finished 9 units of work in 3 days.

⇒ D do 3 units of work in a day.

⇒ D will finish 60 units of work in 20 days.

When C works at 75% of his efficiency,

⇒ Efficiency of C = 3 / 4 × 3 = 2.25

Half of the work = 60 / 2 = 30 units

∴ Number of days taken by C and D to complete half of the work = 30 / (3 + 2.25) = 40 / 7 days

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