Question

A contractor undertakes to dig a canal, $6$ kilometers long, in $35$ days and employed $90$ men. He finds that after $20$ days only $2km$ of the canal have been completed. How many more men must be employed to finish the work in time?

Answer 1

Length of canal $=6km$

In $20$ days canal made $=2km$

Remaining length of canal $=6-2=4km$

Remaining time $=35-20=15$ days

In $20$ days $2km$ canal is made by $=90$ men

In $1$ day $2km$ canal is made by $=90\times 20$ men [Inverse relation between no. of days and people required ]

In $15$ days $2km$ canal is made by $=\frac{90\times 20}{15}$ men

In $15$ days $1km$ canal is made by $=\frac{90\times 20}{15\times 2}$ men

In $15$ days $4km$ canal is made by

$=\frac{90\times 20\times 4}{15\times 2}$ men $=6\times 10\times 4$ men

$=240$ men

$\therefore$ Number of more men to be employed to finish the work in time $=240-90=150$ men.