Question

8) Pooja is twice as efficient as Aarti and takes 90 days less than Aarti to complete the job. Find the time in which they can finish the job together.

Answer 1

2(x-90) = x

2x-180= x

x = 180

180/3 = 60 days

Answer 2

Given

Pooja takes < 90 days of Aarti to complete a job

To find

The time in which both Pooja and aarti can finish the job together

Solution

Assume that Pooja completes the job in 'x' days.

So, Aarti will take '2x' days to complete the same job.

As Pooja takes 90 days less than Aarti, we get

                         x = 2x – 90

                       x - 2x = -90

                              -x = -90  

By solving, we get  X = 90

     Thus, 2x = 2 x 90 = 180

Part of job done by Pooja in 1 day = 1/x = 1/ 90

Part of job done by Aarti in 1 day = 1/2x = 1/180

(Part of job done together in 1 day)

=  (Part of job done by Pooja in 1 day)  +  (Part of job done by      Aarti in 1 day)

= (1/90) + (1/180)

= 3/180

=1/60

   Thus, $\frac{1}{60} ^{th}$ part of whole job will be completed by Pooja and Aarti together in one day.

Therefore, the whole job will be completed in 60 days together.

Answer

 In 60 days , both Pooja and Aarti can finish the job altogether