Question

5 skilled workers can build a wall in 20 days;
8 semiskilled 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 semiskilled and 5 unskilled workers, how long will it take to build the wall ?

• A. 20 days
• B. 18 days
• C. 16 days
• D. 15 days

Answer 1

The correct option is D 15 days

Per day work or rate of 5 skilled workers
$=\frac{1}{20}$

$\Rightarrow$ Per day work or rate of one skill worker
$=\frac{1}{5\times 20}=\frac{1}{100}$

Similarly, Per day work or rate of 8 semiskilled workers
$=\frac{1}{25}$

$\Rightarrow$ Per day work or rate of one semi-skilled worker
$=\frac{1}{8\times 25}=\frac{1}{200}$

And per day work or rate of 10 unskilled workers
$=\frac{1}{30}$

$\Rightarrow$ Per day work or rate of one semi-skill worker
$=\frac{1}{10\times 30}=\frac{1}{300}$

Thus, total per day work of 2 skilled 6 semiskilled and 5 unskilled workers
$=\frac{2}{100}+\frac{6}{200}+\frac{5}{300}=\frac{12+18+10}{600}=\frac{40}{600}=\frac{1}{15}$

Thus, time to complete the work is 15days.

Alternative Method

Let one day work of skilled, semi-skilled & unskilled worker be a,b,c units respectively.

$5a\times 20=8b+25=10c\times 30=Totalunitofwork$
$100a=200b=300c$
$a=2b=3c$

Given, that 2 skilled, 6 semi-skilled and 5 unskilled workers are working. Let they finish the work in 'x' days.
(2a+6b+5c)x = 5a +20
= Total units of work
$(2a+3a+\frac{5}{3}a)x=5a\times 20\frac{20a}{3}x=5a\times 20x=15days$