Question

A group of men decided to do a job in 8 days. But since 10 men dropped out every day, the job get completed at the end of the ${12}^{th}$ day.How many men were there at the beginning ?

• A. $165$
• B. $175$
• C. $80$
• D. none of these

Answer 1

Answer: (A)

$165$

Let number of men be x
$\because ND=N_1{D}_1+N_2{D}_2+N_3{D}_3--------N_{12}{D}_{12}$
$8x=x\times 1+(x-10)\times 1+(x-20)-----(x-110)\times 1$
$8x=12x-10-20-30--------110$
$4x=10+20+30-----110$
$4x=\frac{11}{2}[10+110]$
$4x=660$
$x=165$