+1 vote
98 views
$A$ can complete half work in $7$ days $B$ can do $\dfrac{1}{3}$ of work in $14$ days .while $C$ can complete the $20\%$ of the remaining work in $\dfrac{28}{5}$ days. In how many days $A,B,C$ will complete the work together ?
edited | 98 views
0
$\dfrac{28}{5}$days OR $2\dfrac{8}{5}$ days ?

which one
0
ACTUALLY THIS QUESTION IS FROM A VIDEO LECTURE WHICH SAYS ANSWER IS 84/11 BUT WHEN I SOLVED I GOT 168/17.......SO DONT KNOW ACTUAL ANSWER BUT HOW DID U GOT ????
0
I mean to say C can complete $20\%$ of the remaining work in $\dfrac{28}{5}$ days or $2\dfrac{8}{5}$ days?
0
it is  28/5.(28 upon 5)
+1
Yes, I also got $\dfrac{168}{17} = 9.88$ days

$A$ does $\dfrac{1}{2}^{th}$ work in $7$ days

So, in $\dfrac{7}{\dfrac{1}{2}} = 7 \times 2 = 14$ days $A$ can complete the whole work

$B$ does $\dfrac{1}{3}^{th}$ work in $14$ days

So, in  $\dfrac{14}{\dfrac{1}{3}} = 14 \times 3 = 42$ days $B$ can complete the whole work

Now, remaining work = $\left ( 1 - \dfrac{1}{2} + \dfrac{1}{3} \right ) = \left ( 1 - \dfrac{5}{6} \right ) = \dfrac{6 - 5}{6} = \dfrac{1}{6}$

& $20\%$ of the remaining work = $\dfrac{1}{6} \times 20\% =\dfrac{1}{6} \times \dfrac{1}{5} =\dfrac{1}{30}$

∴ $C$ does $\dfrac{1}{30}^{th}$ work in $\dfrac{28}{5}$ days

So, in $\dfrac{\dfrac{28}{5}}{\dfrac{1}{30}} = \dfrac{28}{5} \times 30 = 28 \times 6 = 168$ days $C$ can complete the whole work

Now, LCM of $(14, 42, 168) = 168$

∴ Total units of work = $168$ units

∴ $A$ can complete $\dfrac{168}{14} = 12$ units of work in $1$ day

$B$ can complete $\dfrac{168}{42} = 4$ units of work in $1$ day

$C$ can complete $\dfrac{168}{168} = 1$ units of work in $1$ day

When $A, B, C$ works together in $1$ day total work done = $12+4+1 = 17$ units

∴ To complete $168$ units $A, B, C$ have to work for $\dfrac{168}{17} = 9.88$ days

∴ To complete the whole work $A, B, C$ have to work together for $9.88$ days.
answered by (2.4k points) 4 8 14
edited
0
THANK U SO MUCH ......
0
great explanation
84/17