Question

A contractor undertakes to build a wall 1000 m long in 50 days. He employs 56 men, but at the end of 27 days, he finds that only 448 m of wall is built. How many extra men must the contractor employ so that the wall is completed in time?

Answer 1

Number of men employed in the beginning = 56
Length of wall = 1000 m
No. of days = 50
In the time of 27 days, only 448 m of wall was completed.
$\therefore$ Remaining period = 50 - 27 = 23 days and length of wall to be completed = 1000 - 448 = 552
Now in 27 days, 448 m long wall was completed by = 1000 m
$\therefore$ in 1 day, 448 m long was completed by $=56\times 27$
in 1 day, 1 m long wall will be completed by $=\frac{56\times 27}{448}m$
and in 23 days 552 m long wall be completed by $=\frac{56\times 27\times 552}{448\times 23}$ men
$=\frac{1\times 27\times 24}{8}=81$ men
$\therefore$ No. of extra men required
= 81 - 56 = 25 men.