Question

To do a certain job B takes 3 times longer than A and C and C twice as long as A and B . Given that A B and C complete the work in 10 days .How much would it take for the three men separately to do it??I challenge if someone can do it ? Answer from the answer sheet is A 24 B 40 & C 30 days!!! best of luck!!!

Answer 1

Easiest of easiest
Let A take x days ,B take y days and C take z days
They all complete the work in 10 days ie their one day work is 1/10
=>1/x+1/y+1/z=1/10..(I)
And it is given B takes 3 times longer as A and C,i.e B do 3 times less work per day then A and C 's one day work
=>1/x+1/z=3/y...(ii)
Also, C takes twice more than A and B i.e 1/x+1/y=2/z..(iii)
Putting eq. (ii) in (I)
3/y+1/y=1/10=>y=40 days
Also putting eq (iii) in eq (I) we get
2/z+1/z=1/10=>z=30 days
Putting value of y and z in eq (I) we get 1/x=5/120=>x =24 days