Time and Work – Problems 1

1.  36 men can do a piece of work in 25 days. In how many days can 30 men do it?

Here , the work is same.. So,
(S X T) / W = (s X t) / w
= >       (S X T) / W = (s X t) / w    [ Cancel W for both sides]
Now, substitute the values…
= >  36 X 25  = 30 X t
= >  (36 X 25) / 30  =  t  => t = 900/3  =  30

2.  32 men can do a piece of work in 15 days working for 6 hours a day. In how many days will 40 men can finish it if they work for 8 hours a day? 32 X 15 X 6  = 40 X d X 8 = 9

3. If 16 men can build a wall of 52 m long in 25 days working for 8 hours a day, in how many days can 64 men build a similar wall of 260m long working for 10hrs a day?

As we know that (Strength X Time) / Work = 1 (Read details Here)

We can write =>

(16 * 200) / 52  =  (64 * X * 10) / 260

=>  X = 25

4. A man engaged 10 laborers to make 320 toys in 5 days. After 3 days he found that only 120 toys were made. How many additional men should he engage to finish the work in time?

here, equate the complete work with the remaining work
(10 X 3) / 120 = (10+X) x 2 / 200
= >   10+X = 25   =>   X = 15

5.  A can do a task in 20 days and B can do it in 30 days. In how many days can they finish it if they work together?

A’s one day’s work = 1/20
B’s one day’s work = 1/30
=> Their one day’s work = (1/20)+(1/30)  =  (3+2)/60  =  5/60  =  1/12
This is their one day’s work TOGETHER.
So, obviously the number of days will be = 12
Short Cut : calculate Product/Sum   =  (20 X 30) / 50 = 12 Thats it