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Three workers Raja, Ravi, and Ratan are appointed to do a job. They together started the job but Ratan left after 3 days when 37% of the job was done. The remaining job was completed by Raja and Ravi in 7 days. The ratio of efficiency of Raja and Ravi is 4 : 5. What will be the number of days required by the slowest worker to complete the entire job alone?

Three workers Raja, Ravi, and Ratan are appointed to do a job. They together started the job but Ratan left after 3 days when 37% of the job was done. The remaining job was completed by Raja and Ravi in 7 days. The ratio of efficiency of Raja and Ravi is 4 : 5. What will be the number of days required by the slowest worker to complete the entire job alone? Correct Answer 30 days

Given:

Ratio of efficiency of Raja and Ravi = 4 : 5

Ratan left after = 3 days

Concept Used:

Total work is LCM of work done by each person.

Formula Used:

Total Work = Efficiency × Time

Calculation:

Let x, y, and z be one day’s work of Raja, Ravi, and Ratan respectively.

Ratio of efficiency of Raja and Ravi = 4 : 5

Total Work = Efficiency × Time

Work done by Ravi and Raja in 7 days = (4 + 5) × 7

⇒ Work done by Ravi and Raja in 7 days = 63

63% work= 63

⇒ Total work = 100% work = 100

Work done by Ravi and Raja in 3 days = (4 + 5) × 3

⇒ Work done by Ravi and Raja in 3 days = 27

Work done by (x + y + z) = 37% of 100

⇒ 3 (4 + 5 + z) = 37

⇒ z = (37 – 27) / 3 = 10 / 3

Days in which Ratan will complete the work = (100 / (10 / 3))

⇒ Days in which Ratan will complete the work = 30

∴ Ratan is the slowest and he can do the work in 30 days.

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