Question

20 workers can finish a piece of work in 30 days after how many days should 5 workers leave the job so that the work is completed in 35 days

Answer 1

Look at it this way:
20 workers ---- do 1 work -----30 days
20 workers ---- in 1 day    ----- 1/30 of whole work
1 worker     ---- in 1 day    ----- 1/600 of whole work
15 workers ---- in 1 day    -----  (1/600)*15= 1/40 of whole work

We know they collectively worked for 35 days overall.

So x+y= 35 -------- eqnⁿ (1)

Suppose that 20 workers worked for x days, and that 15 workers (after 5 left) worked for y days. 

So:
As 20 worked for x days and 15 for y days and completed 1 whole work:

{[x·(1/30)]+ [y·(1/40)]} = 1 

(x/30)+ (y/40)              = 1

(4x+3y)/ 120                = 1

4x+3y                           = 120    eqnⁿ (2)

From eqnⁿ (1):

x+y= 35

x    = 35-y                 

Putting this value in eqnⁿ2:

4 (35 - y)+ 3y = 120
140 - 4y +3y   = 120
y                     =  20 days
x= 35- y ⇒ 15 days

We can infer that:
 
20 workers will first do work for 15 days, then 5 workers will leave and then remaining 15 workers will complete the work in 20 days. Total time taken will be 35 days.

Hence, the answer to the question is 15 days.

Answer 2

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