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X, Y and Z can do a piece of work in 30 days, 45 days and 90 days respectively. In how many days can the work be completed if X is assisted by Y and Z together, on every second day?

X, Y and Z can do a piece of work in 30 days, 45 days and 90 days respectively. In how many days can the work be completed if X is assisted by Y and Z together, on every second day? Correct Answer 20 days

Given- 

Time taken to do the complete work by X, Y, Z is 30 days, 45 days and 90 days respectively.

Concept Used-

Total Work = Efficiency of Worker × Total Time

Calculation- 

Let the total work be 90 units.

Efficiency of X = 90/30 = 3 units/day

Efficiency of Y = 90/45 = 2 units/day

Efficiency of Z = 90/90 = 1 unit/day

Let total time taken to complete the work be 2d days

Here X has worked for all the time but Y and Z has worked for only half the time.

According to the question -

(Efficiency of X) × 2d + (Efficiency of Y + Z) × d = 90

⇒ 3 × 2d + (2 + 1) d = 90

⇒ 9d = 90

⇒ 2d = 20 days

∴ The work can be completed in 20 days.

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