A and B together can finish a piece of work in 15 days; B and C together can finish
the same piece of work in 20 days; C and A together can finish the same piece of
work in 30 days. How long will each take to finish the work alone?
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Answer:
A=40 days
B=40/3 days
C=120 days
Step-by-step explanation:
Given,
A and B together can finish a piece of work in 15 days;
A+B=1/15
B and C together can finish the same piece of work in 20 days;
B+C=1/20
C and A together can finish the same piece of work in 30 days.
C+A=1/30
A+B+B+C+C+A=1/15+1/20+1/30
2(A+B+C)=4+3+2/60
2(A+B+C)=9/60
2(A+B+C)=3/20
(A+B+C)=3/40
substitute A+B=1/15 in the above Equation we get C work alone
C=3/40-1/15
C=9-8/120
C=1/120 days
Substitute C in B+C=1/20 we get B work alone
B=1/20-1/120
B=9/120
B=3/40
substitute C in C+A=1/30 we get A work alone
A=1/30-1/120
A=4-1/120
A=3/120
A=1/40
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