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 who amongst these will take least time

Clearly ##C is the answer.... Take LCM of 12,15,20=60 Therefore a+b=60/12=5,b+c=60/15=4,c+a=60/20=3 ...Total efficiency of a+b+c=5+4+3=12 Equating all three equations such that a+b=5,b+c=4,c+a=3 we get 2(a+b+c)=12 therefore a+b+c=6 now putting value 5 +c=6 Therefore C=6-5=1 and in same equation we get A=2,B=3.....Hence least time will be taken by C