Question

$A$ and $B$ working together can do a work in $6$ days. If $A$ takes $5$ days less than $B$ to finish the work, in how many days $B$ alone can do it alone.

Answer 1

A & B working together do work in $6$ days.

A takes $5$ days less than B.

Let B takes $x$

$\Rightarrow A=x-5$

$\frac{1}{x}+\frac{1}{x-5}=\frac{1}{6}$

$\frac{x-5+x}{x^2-5x}=\frac{1}{6}$

$12x-30=x^2-5x$

$x^2-17x+30=0$

$x^2-15x-2x+30=0$

$x(x-15)-2(x-15)=0$

$(x-2)(x-15)=0$

$\Rightarrow x=2$ or $x=15$

As, $x<5$ so $x=15$

then $A=10$ days $\&B=15$ days

Hence, the answer is $10,15days.$