Efficiency of Hermonie is 25% less than efficiency of Luna, efficiency of Luna is twice the efficiency of Dobbie. Hermione, Luna and Dobbie can complete their mutual assignment in 36 days. In how many days Hermonie independently complete same assignment.

Efficiency of Hermonie is 25% less than efficiency of Luna, efficiency of Luna is twice the efficiency of Dobbie. Hermione, Luna and Dobbie can complete their mutual assignment in 36 days. In how many days Hermonie independently complete same assignment. Correct Answer 108

Given 

If Luna's efficiency is 100 

So, Hermione's efficiency will be 75 

And, Dobbie's efficiency will be 50

They altogether complete an assignment in 36 days 

Concept used 

Work = time × efficiency

Time ∝ 1/ efficiency 

Calculation

Ratio of their efficiency 

Hermione : Luna : dobbie = 75 : 100 : 50 

⇒  3 : 4 : 2

Their total efficiency of 1 day = 9 units 

They altogether complete the assignment in = 36 days 

So, total work = 36 × 9 = 324 units 

Hermione alone complete the assignment in = 324/3 = 108 days

 ∴ Hermione takes 108 days to complete the assignment independently

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