question_answer

A takes 6 days less than B to do a work. If both A and B working together can do it in 4 days, how many days will B take to finish it?

Answer:

Let B can finish a work in x days

so,        A can finish work in \[(x-6)\] days

Together they finish work in 4 days

Now,

\[\frac{1}{x}+\frac{1}{x-6}=\frac{1}{4}\]

\[\frac{x-6+x}{(x)(x-6)}=\frac{1}{4}\]

\[4(2x-6)={{x}^{2}}-6x\]

\[8x-24={{x}^{2}}-6x\]

\[{{x}^{2}}-14x+24=0\]

\[{{x}^{2}}-12x-2x+24=0\]

\[x(x-12)-2(x-12)=0\]

\[(x-12)(x-2)=0\]

Either \[x-12=0\] or \[x-2=0\]

\[x=12\]or \[x=2\], (Rejected)

B can finish work in 12 days

A can finish work in 6 days