Problem Solving

Getting confused with these kind of problems.

Q) 5 workers can print 3000 books in 10 days. How many days will it take 4 apprentices , whose efficiency is 2/3 of a regular worker , take to print 4000 books.

and the same question if it is asked like - efficiency of 4 new workers = 2/3( efficiency of 5 old workers ).

Please explain both the cases step by step.

chaitanyareddy wrote:Getting confused with these kind of problems.

Q) 5 workers can print 3000 books in 10 days. How many days will it take 4 apprentices , whose efficiency is 2/3 of a regular worker , take to print 4000 books.

and the same question if it is asked like - efficiency of 4 new workers = 2/3( efficiency of 5 old workers ).

Please explain both the cases step by step.

Case 1 :

5 can do 3000 in 10 days. In 1 day 5 can do = 3000/10 = 300. ..... All together i.e. 5 working together.
1 worker in 1 day = 300/5 = 60 books in 1 day.
Efficiency of 1 apprentice = 2/3 (60) = 40 books in 1 day.
4 can do 40*4 in 1 day = 160.
160*x = 4000. Therefore x = 25 days to do 4000 books.

Case 2 :

Total efficiency of 4 workers = 2/3 of total efficiency of 5 workers.
total 4 workers in 1 day = 2/3 total of 5 in one day.
= 2/3 (300)
= 200 in 1 day.

200 * x = 4000. Therefore x = 20 days.

Hope it helps.

This is how I do it :

5W ---------- 3000 books ---------- 10 days

5A ---------- 3000 books ----------10/(2/3) = 15 days
we know the efficiency of apprentice is less so they require more days to print the same number of books as workers.

5A ---------- 1 book ---------- 15/3000 days
we know as the no. of books decreases, the number of days will decrease.

5A ---------- 4000 books ---------- (15/3000)*4000 days = 20 days
As the number of books increases, the number of days increases so multiply.

1A ---------- 4000 books ---------- 20*5 = 100 days
1 apprentice will require more days to print the same no. of books as 5, so multiply.

4A ----------- 4000 books ----------- 100/4 = 25 days

chaitanyareddy wrote:Getting confused with these kind of problems.

Q) 5 workers can print 3000 books in 10 days. How many days will it take 4 apprentices , whose efficiency is 2/3 of a regular worker , take to print 4000 books.

and the same question if it is asked like - efficiency of 4 new workers = 2/3( efficiency of 5 old workers ).

Please explain both the cases step by step.

5 workers can do the job in 10 days,
now i if there efficiency decrease by 2/3 , they will take 3/2 of time to the job, that will be 10 * 3/2 = 15 days,
They can print 3000 books in 15 days with 2/3 efficiency { if work is increased by 1/3 they will also 4/3 of the time, 15 * 4/3 = 20 days, }

Now there were 5 there ,, If there were 4 workers , it means 4/5 of 5, it means they will take 5/4 of 20 days,
20 * 5/4 = 25 days.