1.

A and b can do a piece of work in 10 day b and c is 15 day and c and a in 20 then c alone can do same work

Answer»

A and B can do a piece of work in 10 days
so, A+B = 10
one day work of A and B
A+B = 1/10.............(1)

B and C can do it in 15 days
so, B + C = 15
one day work of B and C is
B+C = 1/15..............(2)

A and C can do it in 20 days
so, A+C = 20
one day work of A and C is
A+C = 1/20...........(3)

sum all three EQUATIONS (1), (2), (3)
(A+B) + (B+C) + (A+C) = (1/10)+(1+15)+(1/20)
2A + 2B + 2C = (1/5)((1/2)+(1/3)+(1/4))
2(A+B+C) = (1/5)((6+4+3)/12)
2(A+B+C) = 13/60
A+B+C = 13/120..............(4)

substitute (1) in (4)
(1/10) + C = 13/120
C = (13/120) - (1/10)
C = (13-12)/120
C = 1/120
one day work of C is 1/120

whole work DONE by C in 120 days

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