Question

a and b can do a piece of work in 12 days , b and c in 15 days , And c and a in 20 days .how much time will alone take to finish the job ?

Answer 1

a+b=12------(1)
b+c=15-----(2)
c+a=20------(3)
(3)-(1)=>c-b=8----(4)
(2)+(4)=>2c=23
=>c=11.5
(3)=>a=8.5
(1)=>b=3.5

Answer 2

Given:

A and B can do a piece of work in = 12 days

Work done by A and B in 1 day = 1/12

B and C can do a piece of work in = 15 days

Work done by B and C in 1 day = 1/15

A and C can do a piece of work in = 20 days

Work done by A and C in 1 day = 1/20

Solution:

On adding A, B and C we get,

2(A+B+C)’s one day work

= 1/12 + 1/15 + 1/20

= (5+4+3)/60 (by taking LCM for 12, 15 and 20 which is 60)

= 12/60

= 1/5

A+B+C one day work = 1/(5×2) = 1/10

Knowing that:

Work A can do in 1 day

= (A+B+C)’s 1 day work – (B+C)’s 1 day work

= 1/10 – 1/15

= (3-2)/30 (by taking LCM for 10 and 15 which is 30)

= 1/30

Answer:

∴ A alone can finish the work in = 1/(1/30) = 30days.