Question

$2$ men and $6$ boys can do work equivalent to $15$ days. With similar efficiency, $1$ man and $4$ boys can do another work equivalent to $12$ days.
Are these statements correct?

• A. Yes. There exist a solution.
• B. No. There is no feasible solution.

Answer 1

The correct option is B No. There is no feasible solution.

Let the work done by a man is represented by $x$ workdays.
And the work done by a boy is represented by $y$ workdays.

As per the first statement,
$2$ men will do $2x$ workdays, and $6$ boys will do $6y$ workdays.
$\Rightarrow 2x+6y=15...\left(a\right)$

As per the second statement,
$x+4y=12...\left(b\right)$

Let's solve these equations by the elimination method.
Mulitply $\left(b\right)$ by $2$ and subtract from $\left(a\right).$

$2x+6y-2(x+4y)=15-2\times 12$
$\Rightarrow 6y-8y=15-24$
$\Rightarrow 2y=9$
$\Rightarrow y=4.5$
$\therefore$ A boy can do work equivalent to $4.5$ work days.

Substituting this in $\left(b\right)$ we get,
$x+4\left(4.5\right)=12\Rightarrow x+18=12\Rightarrow x=-6$
$x$ cannot have a negative value.

$\therefore$ The given statements are not correct.