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# Arithmetic Aptitude :: Time and Work

## 3. A and B can finish a piece of work in 20 days .B and C in 30 days and C and A in 40 days. In how many days will A alone finish the job

Explanation :

Find one day work for all three
(A+B)'s 1 day work = 1/20 ----(1)
(B+C)'s 1 day work = 1/30 ----(2)
and (C+A)'s 1 day work = 1/40 ----(3)
2(A+B+C) 1 day work = (1/20 + 1/30 + 1/40)
=> (A+B+C) = (6+4+3)/2*120
=> (A+B+C) = 13/240 -----------(4)
By eq. (2) and (4)
A + 1/30 = 13/240
=> A = 13/240 - 1/30 = (13-8)/240 = 1/48
then A's 1 day work = 1/48
so A alon can finish the job = 48 days