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