2.4k views

$5$ skilled workers can build a wall in $20$ days; $8$ semi-skilled workers can build a wall in $25$ days; $10$ unskilled workers can build a wall in $30$ days. If a team has $2$ skilled, $6$ semi-skilled and $5$ unskilled workers, how long it will take to build the wall?

1. $20$ days
2. $18$ days
3. $16$ days
4. $15$ days

edited | 2.4k views

D. $15$ days

$1$ skilled person can do $\frac{1}{20 \times 5} = 1/100$ of work in $1$ day, so $2$ skilled person do $2/100$ of work in a day.

Similarly, $6$ semi-skilled and $5$ unskilled person can do $6/200$ and $5/300$ of work respectively in $1$ day.

So, together they do $\frac{2}{100}+\frac{6}{200}+{5}{300} = \frac{1}{15}$ of work together in $1$ day, which gives required number of day to complete the work $= 15.$
by Active (3.5k points)
selected by
0
5 / 300 instead of 5300

btw amazing solution
+1 vote

D: 15 days

5 skilled:- 20 days, so 1 skilled done in 20*5 days = 100 days

2 skilled done in 100/2= 50 days.   , similarly, 6 semi-skilled done in 200/6

similarly, 5 unskilled done  in 300/5 = 60

M: Manpower, R: Rate, T : Time, W: Work done

M        2 skilled (s)                     6 semi-skilled (ss)           5 unskilled (us)              s+ ss+ us

R        12                                            18                                        10                            40

T        50  days                            200/6 days                       60 days                             x

W       600                                 600                                   600                                  600

take LCM(50,100/3,30) = [ LCM(50,200,30) / HCF(1,6,1) ] = 600/1= 600

Rate = W/T

Rate of s+ss+us = 12+18+10= 40

x=600/40 = 15 days

by Junior (987 points)
edited