Question 975770
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A and B can do a piece of work in 6 days, B and C together in 10 days, C and A together in 7 1/2 days.
in how many days can C individually completes the work?
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<pre>
Let  'a'  be the rate of work for A;
     'b'  be the rate of work for B;
     'c'  be the rate of work for C.


From the problem, we have this system of equations 

    a + b = {{{1/5}}},      (1)

    b + c = {{{1/10}}},     (2)

    a + c = {{{1/7.5}}}.    (3)


Add equations (1), (2) and (3).  You will get

    2(a + b + c) = {{{1/5}}} + {{{1/10}}} + {{{1/7.5}}}.    (4)


Multiply both sides of (5) by 60.  Notice that  {{{60/7.5}}} = 8.  You will get

    120*(a + b + c) = 12 + 6 + 8 = 24,

which implies

    a + b + c = {{{24/120}}},

or

    a + b + c = {{{1/5}}}.    (5)


Now, to find 'c', subtract equation (1) from equation (5).  You will get

    c = {{{1/5}}} - {{{1/6}}} = {{{(6-5)/30}}} = {{{1/30}}}.


Hence, the C's rate of work is 1/30 of the job per day,
which means that C can complete the entire job in 30 days working alone.


<U>ANSWER</U>.  C can complete the entire job in 30 days working alone.
</pre>

Solved.