Question

A contractor Abhay Singh employed some men to do a piece of work which can be done by 16 men in 14 days.At the end of 5 days, 7 of the men stopped working and 3 days later half of the remainder stopped working; the rest finished the work in 5 days.What is the number of men originally employed?

• A. $25$
• B. $27$
• C. $29$
• D. $33$

Answer 1

Answer: (A)

$25$

16 men can complete the work in 14 days.
Let initially x men were employed using $M_1{D}_1=M_2{D}_2$
ATQ
$16\times 14=5x+3(x-7)+5\frac{(x-7)}{2}$
$224=\frac{21x-42-35}{2}$
$21x=448+77$
$x=\frac{525}{21}=25$