Question

Raksha can do a work in 27 days while Esther takes 45 days to do it herself. They start working together, but Raksha leaves 9 days before the work is over. How many days does Esther work?
1. 18
2. 27
3. 13.5
4. 22.5

Answer 1

Correct Answer - Option 4 : 22.5

Given:

Raksha completes work in 27days.

Esther completes work in 45days.

Raksha leaves 9 days before the work is over.

Formula Used:

Efficiency = total work / time taken

Total work = LCM of time taken

Calculation:

Total work = LCM of time taken

⇒ Total work = LCM of 27days and 45 days.

⇒ Total work = 135units.

⇒ Efficiency_(Raksha) = 135 / 27 = 5

⇒ Efficiency_(Esther) = 135/45 = 3

Efficiency	Subject	Time taken	Total work
5	Raksha	27	135
3	Esther	45	135

Raksha leaves 9 days before the work is over.

last 9  days Esther alone worked.

⇒ Total units of work completed by Esther in 9days

⇒ 9× 3 = 27 units

units of work completed by Raksha and Esther together,

⇒ 135 - 27 = 108 units

108 units of work completed by Raksha and Esther together,

⇒ Time taken by Raksha and Esther together = 108/8

⇒ Time taken by Raksha and Esther together  = 13.5 days.

⇒ Esther worked for 13.5days + 9days = 22.5days  

∴ Esther works for 22.5 days.