Question

Three workers rahul,sumit and ajay undertook a work a work to dig a pit. When sumit and rahul work together, they take 6 days to dig the pit. However, when rahul and ajay work together, they take 9 days to finish the same task. When rahul worked alone, he took thrice as much time that would be taken by all three working together. How much time is required if they all work on the same task

Answer 1

Answer:

24/5 days

Step-by-step explanation:

Hi,

Let 'x' be the number of days Rahul working alone takes to complete the task

=> In 1 day, Rahul does 1/x th of work

Let 'y' be the number of days Sumit working alone takes to complete the task

=> In 1 day, Sumit does 1/yth of work

Let 'z' be the number of days Ajay working alone takes to complete the task

=>In 1 day, Ajay does 1/zth of work.

Given that Sumit and Rahul working together , they take 6 days to dig the

pit.

=> 6(1/x + 1/y) = 1

=> 1/x + 1/y = 1/6----(1)

Given that Rahul and Ajay take 9 days to finish the same task

=> 9(1/x + 1/z ) = 1

=> 1/x + 1/z = 1/9-----(2)

Adding (1) + (2), we get 2/x + 1/y + 1/z = 5/18----(3)

If Rahul works alone, he takes thrice time taken by all 3 working together

=> 1/x = 1/3*(1/x + 1/y + 1/z)

=>1/x + 1/y + 1/z = 3/x-----(4)

Using (3), we get 1/x = 1/3*(1/x + 5/18 - 2/x)

=> 3/x = 5/18 - 1/x

=> 4/x = 5/18

=> x = 72/5 days = 14 2/5 days

If all work together, they take 1/(1/x + 1/y + 1/z) number of days, but using (4)

1/(3/x) = x/3 = 24/5 = 4 4/5 days

Hence , if they all work together on the same task, they take 24/5 days to

finish.

Hope, it helped !