Question

Raksha can complete a piece of work
in 27 days while Esther takes 45 days
to complete the work. They start
working together, but Raksha leaves
9 days before the work gets over. For
how many days does Esther work?​

Answer 1

Answer:

15

Step-by-step explanation:

Raksha =27 days=9

Esther=45 days =x

27x=9*45

27x= 405

x=405/27

x=15

Esther takes 15 days

Answer 2

Esther worked for 22.5 days.

Step-by-step explanation:

Given,

Raksha can complete a piece of work  in 27 days,

So, the one day work of Raksha = $\frac{1}{27}$,

Similarly, Esther takes 45 days  to complete the work,

The one day work of Esther = $\frac{1}{45}$

Total one day work = $\frac{1}{27}+\frac{1}{45}$

$=\frac{5+3}{135}$

$=\frac{8}{135}$

Consider the work is completed in x days,

Since, for 9 days before completion of work they work together,

That is, total work for (x-9) days = Number of days she worked × One day work,

$= (x-9)\times \frac{8}{135}$

Now, remaining part of work is completed by Esther alone in 9 days,

So, remaining part of work = $9\times \frac{1}{45}=\frac{1}{5}$

∵ Total part = 1

$\implies (x-9)\times \frac{8}{135} + \frac{1}{5}=1$

$\frac{8x-72}{135}+\frac{27}{135}=1$

$8x-72+27=135$

$8x - 45 = 135$

$8x = 180$

$\implies x =\frac{180}{8}=22.5$

Hence, Esther worked for 22.5 days.

#Learn more:

Ram and Shyam work on a job together for four days and complete 60% of it. Ram takes leave then and Shyam works for eight

https://brainly.in/question/8175769