A and B can do a piece of work in 10 hours, B and C in 12 hours and Cand A in 15 hours. How long will
they take if they work together? How long will each take to complete the work independently?
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Solution :-
A and B can do a piece of work in 10 hours.
(A + B)'s one hour work = 1/10
B and C in 12 hour
(B + C)'s one hour work = 1/12
C and A in 15 hours
(A + C)'s one hour work = 1/15
Now,
Adding the total's one hour work = 1/10 + 1/12 + 1/15
=> (A + B + B + C + C + A) = (6 + 5 + 4)/60
=> 2(A + B + C)= 15/60
=> ( A + B + C) = 15/(60 × 2) = 1/8
They work together can do it in 8 days.
1/A = 1/8 - 1/12
=> 1/A = (3 - 2)/24
=> 1/A = 1/24
=> A = 24
A alone do it in 24 days .
1/B = 1/8 - 1/15
=> 1/B (15 - 8)/120
=> 1/B = 7/120
=> B = 120/7 = 17 (approx.)
B alone do it in 17 days .
1/C = 1/8 - 1/10
=> 1/C = (5 - 4)/40
=> 1/C = 1/40
=> C = 40
C alone do it in 40 days.
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