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A piece of work is done by three persons Jadhav, Kumar and Shukla in 5 days in the following manner: Jadhav works for whole time, Kumar only on the first two days and Shukla only on the last three days. This work could have been done by Kumar and Shukla in 6 days without involving Jadhav. If Kumar and Shukla working together can do as much work in 2 days as Jadhav can do in 3 days, then find how long will it take for each one to do this work alone?

A piece of work is done by three persons Jadhav, Kumar and Shukla in 5 days in the following manner: Jadhav works for whole time, Kumar only on the first two days and Shukla only on the last three days. This work could have been done by Kumar and Shukla in 6 days without involving Jadhav. If Kumar and Shukla working together can do as much work in 2 days as Jadhav can do in 3 days, then find how long will it take for each one to do this work alone? Correct Answer 9, 18, 9

Let,

Jadhav completes the work in = ‘a’ days

Kumar completes the work in = ‘b’ days

Shukla completes the work in = ‘c’ days

⇒ Jadhav’s 1 day’s work = 1/a

⇒ Kumar’s 1 day’s work = 1/b

⇒ Shukla’s 1 day’s work = 1/c

According to the question, Jadhav works for 5 days, Kumar for 2 days, Shukla for 3days and complete the work.

⇒ (5/a) + (2/b) + (3/c) = 1      ----(1)

Also, Kumar and Shukla together complete the work in 6 days.

⇒ 6 = 1

⇒ 1/b + 1/c = 1/6      ----(2)

According to the question,

Kumar and Shukla’s 2 day’s work = Jadhav’s 3d ay’s work.

⇒ 2 = 3/a

⇒ 2/6 = 3/a

⇒ a = 9 days

Putting a= 9 in equation (1) we get,

⇒ (5/9) + (2/b) + (3/c) = 1

⇒ (2/b) + (3/c) = 4/9      ----(3)

Solving equations (2) and (3) we get, b = 18 and c = 9

∴ a = 9, b = 18 and c = 9

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