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X can complete a piece of work in 48 days, Y in 72 days and Z in 96 days. They started the work together but X and Z left six days and nine days before the completion of the work respectively. In how many days was the work completed?
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X can complete a piece of work in 48 days, Y in 72 days and Z in 96 da...
Given:

  • X can complete a piece of work in 48 days

  • Y can complete a piece of work in 72 days

  • Z can complete a piece of work in 96 days

  • X and Z left 6 days and 9 days before the completion of the work respectively


To find: In how many days was the work completed?

Concept Used:

  • We will use the formula Time = Work/Rate to solve the problem.

  • Let the total work to be completed be 1 unit.

  • Then, the work done by X in a day is 1/48, the work done by Y in a day is 1/72 and the work done by Z in a day is 1/96.

  • Let the total time taken to complete the work be D days.

  • Then, the work done by X in D days is (D-6)/48, the work done by Y in D days is D/72 and the work done by Z in D days is (D-9)/96.

  • As they started the work together, the total work done in D days is 1.



Solution:

  • The work done by X, Y and Z in one day is 1/48, 1/72 and 1/96 respectively.

  • Work done by X, Y and Z in D days = D(1/48 + 1/72 + 1/96)

  • Work done by X in D-6 days = (D-6)/48

  • Work done by Z in D-9 days = (D-9)/96

  • Work done by X, Y and Z in D days - Work done by X in D-6 days - Work done by Z in D-9 days = 1

  • D(1/48 + 1/72 + 1/96) - (D-6)/48 - (D-9)/96 = 1

  • Solving the above equation, we get D = 32 days.



Answer:

  • The work was completed in 32 days.

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X can complete a piece of work in 48 days, Y in 72 days and Z in 96 days. They started the work together but X and Z left six days and nine days before the completion of the work respectively. In how many days was the work completed?
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