PROBLEM ON TIME & WORK –
Example.1) 4 men and 4 boys can do a piece of work in 3 days, while 2 men and 5 boys can finish it in 4 days. How long would it take 1 boy to do it.
Ans.) Let, 1 man can do the work in x days and 1 boy can do it in y days.
1
Then, 1 man’s 1 day’s work = ------
x
1
Then, 1 boy’s 1 day’s work = ------
y 1
Now, (4 men’s 1 day’s work) + (4 boy’s 1 day’s work) = -------
3
4 4 1
------- + ------- = -------
x y 3
1 1 1
------- + ------- = ------- …………………….(i)
x y 12
1
Now, (2 men’s 1 day’s work) + (5 boy’s 1 day’s work) = -------
4
2 5 1
------- + ------- = ------ ………………………(ii)
x y 4
Multiplying (i) by 2, we get –
2 2 1
------- + ------- = ------- …………………….(iii)
x y 6
Subtracting (iii) from (ii), we get –
2 5 2 2 1 1
------ + ------- - ------- - ------- = ------ - ------
x y x y 4 6
(5 – 2) 3 – 2
=> ---------- = ---------
y 12
3 1
=> ------ = -------
y 12
1 1
=> ------- = -------
y 36
=> y = 36
Substituting the value y = 36 in (i), and we get -
1 1 1
------- + ------- = -------
x y 12
1 1 1
=> ------ + ------ = -------
x 36 12
1 1 1
=> ------- = ------- - -------
x 12 36
1 3 – 1
=> ------- = ----------
x 36
1 2 1
=> ------- = ------- = -------
x 36 18
=> x = 18
So, 1 boy can do it in 36 days and 1 man can do it in 18 days. (Ans.)