A nd B can complete a certain task in 45 days nd 60 days respectively . Both worked together for 15 days then B left .The remaining task was completed by A nd C together in next 7 1\2 days .In how many days can C alone do 50% of the same task?
Answers
Answer:
20
Step-by-step explanation:
A- 45
B- 60
LCM of A and B is 180
both work for 15 days
Step-by-step explanation:
lets take total work = W
work done by A in single day =W/45
work done by B in single day= W/60
lets take work can done by C alone = X
work done by C in single day =W/X
work done by A and B together for 15 days
work done by A and C together for 15/2 (which means 7 1/2days)
there for ,
15(w/45 + w/60) + 15/2(w/45 + w/x) = W
=> 15w/45 + 15w/60 + 15w/90 + 15w/2x =w
=> 15/45 + 15/60 + 15 /90 +15/2x = 1 ( w is common factor, so it cancelled)
=> 1/3 + 1/4 + 1/6 + 15/2x =1
=> 3/4 + 15/2x =1 (1/3+1/4+1/6 =3/4)
=> 15/2x = 1 - 3/4
=> 15/2x = 1/4
=> (15 * 4)/2 = x
=> x = 30
C can alone do the work in 30 days
and C can alone do 50% of the work in 15 days..
answer is 15