Question

A group of men decided to do a job in 8 days. But since 10 men dropped out after 1st day, 2 more men
dropped out after 2nd day, 2 more men dropped out after 3rd day and so on, the job got completed at the
end of 12th day. How many men were there at the beginning?
(1) 55
(2) 56
(3) 57
(4) 58​

Answer 1

Answer:

(1) 55 answer

steps

hence required answer is 55 mens

Answer 2

TIME-Work Problem

Let the number of men in the beginning is x.

The work was completed on 12th day, means some number of men work on every day for these 12 days.

Number of days that was decided to complete the job $=8$

So following the pattern given in the question for men leaving the job each day, we can infer that,

$nd=n_1d_1+n_2d_2+n_3d_3+\_+\_+\_n_{12}d_{12}$

$\implies 8x=x\times 1+(x-10)\times 1+(x-12)\times1+(x-14)\times1+\_+\_+\_(x-30)\times1$

$\implies 8x=x+x-10+x-12+x-14+\_+\_+\_+x-30\\\\\implies 8x= (x+x+x+x+\_+\_+\_+12\ times)-(10+12+14+16+18+20+22+\_+\_+30)$

$\implies 8x=12x-220\\\\\implies220=4x$

$\implies x=55$

Hence, number of people in beginning was 220.