10th Class Mathematics Solved Paper - Mathematics 2017 Outside Delhi Set-III

  • 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


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