Question 1201576
.
116.6% of the work done by B at 10% of his efficiency is equal to 
25% of the work done by A when he work at 75% more than his 
efficiency. Both A and B working together can complete the work in 6 
days. Find the time taken by B to complete the whole work ?
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            This problem is on a  "rate of work ".



<pre>
Let x be the A's rate of work; 

Let y be the B's rate of work.


The first statement "116.6% of the work done by B at 10% of his efficiency is equal to 
                     25% of the work done by A when he work at 75% more than his efficiency"
means that

    1.166*(0.1y) = 0.25*(1+0.75)x.


Also, understanding that the problem's creator wanted to say " 116.6...% " instead of 116.6% 
(kind of joke from his side), we can rewrite this equation in the form
 ~~~~~~~~~~~~~~~~~~~~~~~~~~

    1{{{1/6}}}*{{{(1/10)*y}}} = {{{(1/4)*(7/4)x}}},

or

    {{{(7/6)*(1/10)y}}} = {{{(1/4)*(7/4)x}}}.


Reducing the factor 7 in both sides, we get

    {{{y/60}}} = {{{x/16}}},  or  {{{y/15}}} = {{{x/4}}},  or  x = {{{(4/15)*y}}}.    (1)



The second statement "Both A and B working together can complete the work in 6 days"                     
means that

    x + y = {{{1/6}}}.



Substitute here  x = {{{(4/15)*y}}}  from (1),  and you will get

    {{{(4/15)y}}} + y = {{{1/6}}},

or

    {{{(19/15)y}}} = {{{1/6}}},  y = {{{((1/6))/((19/15))}}} = {{{15/(6*19)}}} = {{{5/(2*19)}}} = {{{5/38}}}.


It means that B can complete the job in  {{{38/5}}} = 7{{{3/5}}}  days working alone.    <U>ANSWER</U>
</pre>

Solved.



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So, &nbsp;this problem is partly &nbsp;" a joke ", &nbsp;but it is a bit a crocked/curved joke.


Me, &nbsp;from my side, &nbsp;tried to teach you on how to solve this problem and similar problems in a rational way.


<pre>
"A rational way" in this case means "saying minimum words and writing minimum equations,
                                     but still enough in order for everything be clear".
</pre>