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A can complete a piece of work $3$ times as fast as B.If A and B together can complete the work in $6$ days.

How many days would B alone take to complete the work?

options given:

a)$8$ b)$12$ c)$24$ d)$4$

My Approach:

Let A take x Days and B take $3x$ Days

A:B=$3$:$1$ Efficiency

Therefore, time taken is $x$:$3x$

Let A take x Days and B take $3x$ Days

A+B=$6$ days

So,Now A take x/x+$3$x=x/4x*$6$=$3$/$2$

Now B take $3x$/$4x$=$3$/$4$*$6$=$9$/$2$

This Approach is wrong i don't know why and i coulno't solve through other approaches.

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  • $\begingroup$ What is the book answer? $\endgroup$ – NoChance Sep 13 '15 at 16:16
  • $\begingroup$ @EmmadKareem It is 24. $\endgroup$ – justin takro Sep 13 '15 at 16:59
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Let $x$ be the fraction of the work that $B$ does in one day. A does $3x$ in one day. They both do it in 6 days so $6(x+3x)=1$ and thus $x=1/24$. So $B$ needs $24$ days.

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