efficiency of Kanchan is 4 times to that of henna if they will complete the work in 24 days by working together then how many days can Hina alone complete the work
Answers
If Kanchan’s efficiency is 4 times than that of Hina, and they together work in 24 days, then Hina alone would take 120 days to complete the task.
Step-by-step explanation:
It is given that, Kanchan is 4 times more efficient than Heena.
Since Efficiency ∝ [1/Time taken]
So, if Kanchan alone takes “x” days to complete the task then the time taken by Heena would be “4x” days.
Amount of work done by Kanchan in 1 day = 1/x
Amount of work done by Hina in 1 day = 1/4x
Also given that they when working together can finish the work in 24 days
The amount of work done by both Kanchan and Hina together in 1 day is
1/x + 1/4x = 1/24
⇒ [4x+x]/4x² = 1/24
⇒ 5x/4x² = 1/24
⇒ 5/4x = 1/24
⇒ 4x = 24 * 5
⇒ x = 5 * 6
⇒ x = 30 days
∴ 4x = 4 * 30 = 120 days
Hence, Hina alone would complete the task in 120 days.
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