Question

Twenty five workers were employed to complete a compound wall in 12 days. Five workers left after working for four days . The remaining 20 workers completed the work, In how many days was the total job completed?
a.15 days
b.16 days
c.14 days
d.18 days

Answer 1

Hint: As we are given that 25 workers can complete it in 12 days then the product of the number of workers and number of days gives the total work. And we are given that five workers leave after 4 days , so 25 workers work for 4 days and 20 workers work for y days . Equating the total work we get the value of y and adding the four days to it we get the required number of days .

Complete step-by-step answer:
We are given that 25 workers can complete the work in 12 days
Hence the total work is equal to the product of the number of days and the number of workers
Total work = No. of workers * No . of days
                     =25*12………(1)
Now we are given that after working for four days five workers left , and the remaining 20 workers worked for y days to complete the work
Total work = ( 25 * 4 ) + (20 * y )………..(2)
Equating (1) and (2)
$
   \Rightarrow (25*12) = (25*4) + (20*y) \\
   \Rightarrow 300 = 100 + 20y \\
   \Rightarrow 300 - 100 = 20y \\
   \Rightarrow 200 = 20y \\
   \Rightarrow y = \dfrac{{200}}{{20}} = 10 \\
$
Therefore this tells us that the 20 workers take 10 more days to complete the work
Therefore the total number of days = 4 + 10 = 14 days
The correct option is c

Note: Points to remember while solving these types of questions:-
1.If a person does a work in ‘r’ days, then in 1 day- $\dfrac{1}{r}$ th of the work is done and if $\dfrac{1}{s}$th of the work is done in 1 day, then the work will be finished in ‘s’ days. Thus working together both can finish $\dfrac{1}{h}\left( {\dfrac{1}{r} + \dfrac{1}{s} = \dfrac{1}{h}} \right)$ work in 1 day & this complete the task in ’h’ hours.
2.The same can also be interpreted in another manner i.e. If one person does a piece of work in x days and another person does it in y days. Then together they can finish that work in xy/(x+y) days.
3.In case of three persons taking x, y and z days respectively, They can finish the work together in xyz/(xy + yz + xz) days.