Question

a b c can do a piece of work in 10 days.a and b can do it alone in 24 and 30 days.a and b worked together for 12 days.in how many days c alone complete the remaining work

Answer 1

The time taken by c to complete the work is 4 days

Answer 2

a+b+c do a work in 10 days

therefore a+b+c one day's work =1/10; a+b+c=1/10.......(i)

a alone can do in 24 days; therefore a's one day work =1/24; a=1/24....(ii)

b alone can do in 30 days; therefore b's one day work =1/30; b=1/30....(iii)

a+b=1/24+1/30.......(iv)

a+b one day's work = 1/24+1/30; therefore in 12 days a+b do 12/24+12/30=9/10 part of work.; therefore work remaining 1-9/10=1/10

Now substituting the value of a+b in equation (i), we get 1/24+1/30+c=1/10

c= 1/10-1/24-1/30=1/40 which is c's one day work..

c does the complete work in 40days ;

therefore c does the remaining 1/10th part of work in 1/10*40= 4 days.

Hope this helps!!