1.

If the ratio of working efficiency of X and Y is 6 ∶ 5 and that of Y and Z is 5 ∶ 4. If X can complete the work in 4 days, then in how many days the total work will be completed if X and Y are assisted by Z on every alternate day?1. 21/11 days2. 3 days3. 28/15 days4. 2 days

Answer» Correct Answer - Option 3 : 28/15 days

Given:

Ratio of work efficiency of X and Y is 6 ∶ 5 and that of Y and Z is 5 ∶ 4.

X can complete the work in 4 days. 

Z assists X and Y on every alternate day.

Concepts used:

Time = Work/Efficiency

Efficiency = Work/Time

Work = Efficiency × Time

Calculation:

Ratio of work efficiency of X and Y is 6 ∶ 5 and that of Y and Z is 5 ∶ 4. 

X ∶ Y = 6 ∶ 5

Y ∶ Z = 5 ∶ 4

⇒ X ∶ Y ∶ Z = 6 ∶ 5 ∶ 4

X can complete the work in 4 days. 

Work = Efficiency × Time

Total work done by X = 6 × 4 = 24 unit

Time = Work/Efficiency

First day work of X and Y = 6 + 5 = 11 unit 

Remaining work = 24 – 11 = 13 unit

Second day work of X, Y and Z = 6 + 5 + 4 = 15 unit

15 unit work is done by X, Y and Z in 1 day.

Time taken by X, Y and Z to complete 13 unit work = 13/15 

Total time taken by X, Y and Z = 1 day + 13/15 days = 28/15 days

∴ X, Y and Z took 28/15 days to complete the work together if X and Y are assisted by Z on every alternate day.



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