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The ratio of efficiencies of 3 labours is 1 ∶ 2 ∶ 3. On working together, they can finish the work in 30 days. If 1st and 3rd labours are double their efficiency and 2nd labour reduces to half, then in how many days the work will be finished?

The ratio of efficiencies of 3 labours is 1 ∶ 2 ∶ 3. On working together, they can finish the work in 30 days. If 1st and 3rd labours are double their efficiency and 2nd labour reduces to half, then in how many days the work will be finished? Correct Answer 20 days

Given:

Ratio of efficiencies of 3 labours say A, B and C is 1 ∶ 2 ∶ 3.

Efficiency of A and C is double and B's becomes half.

A, B and C can complete the work in 30 days.

Formula used:

Total work = Number of person × Average efficiency × Number of days

M1D1H1/W1 = M2D2H2/W2      (where M is number of men, D is number of days, H is number of hours and W is amount of work/wages.)

Calculations:

Let the efficiencies of A, B and C be 1unit/day, 2 units/day and 3 units/day respectively.

Let the number of days required to complete the work after change in efficiencies be 'd days'.

Let the total work be '1'.

Initial average efficiency = (1 + 2 + 3)/3

⇒ 2 units/day

Final average efficiency = (2 + 1 + 6)/3

⇒ 3 units/day

According to question,

⇒ (3 × 2 × 30)/1 = (3 × 3 × d)/1

⇒ d = 20 days

∴  The number of days required to complete the work after change in efficiencies is 20.

 

 

 

 

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