Bunuel
Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?
A. 46/9
B. 50/9
C. 50/11
D. 36/7
E. 210/41
Hi,
firstly it is a tough Q.. if one is clueless where to start, we can work on the info and easily eliminate three choices B,C, and D, and E too can be eliminated after a bit of thought...IN first case A working for 6 days and B for 4 days, work is completed and in second case A for 4.5 days and B for 6 days, wk gets completed..
so if we combine A for 10.5 days and B for 10 , wk can be completed twice ...
so wk to be completed once, A requires to work for 5.25 days and B for 5 days...
what can we make out ..
1) if both A and B work for 5 days, the work will not be completed, as we have to add .25 day work of B to it.. C (50/11)<5 is out...
2) work will be completed before (5+5.25)/2 days, as work of .25 days of A is being done by both together and A is faster than B..
so total time will be greater than 5.125 and should be less than 5.25, when A is faster than B ..
so following can be eliminated
A 46/9=5.111 <5.125
B 50/9=5.55>5.25
E 210/41= 5.122<5.125..
D 36/7=5.14...CORRECT .. between 5.125 and 5.25 is the answer..answer can also be arrived at by proper work-time method.IN first case A working for 6 days and B for 4 days, work is completed
or 6/a +4/b=1..(i)
and in second case A for 4.5 days and B for 6 days, wk gets completed..
so 4.5/a+ 6/b=1..(ii)
or 6/a +4/b= 4.5/a+ 6/b...
we get a=3b/4 here ..
substitute this value in (i)..
24/3b +4/b=1...
this will give us b as 12..
so a= 3b/4=9..
we have to find 1/a+1/b as one day work of both..1/12 + 1/9= (3+4)/36= 7/36..
so time taken = 36/7
D