Question

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?​

Answer 1

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