A B C can do a piece of work in 12 days, A can do twice Than B ..C can do thrice B. find in how many days C alone di
Answers
Answer:
6
Step-by-step explanation:
A+B+C=12
2B+B+3B=12
6B=12
B=2
C=3B
C=3×2=6
Step-by-step explanation:
Workdone=rateoftheperson×timetaken
W=r×t=rt
Now if A and B are working together, the work done is given by
W=(rA+rB)tAB
where rA is the rate of A and rB is the rate of B and tAB is time taken for A and B working together to finish the work.
tAB=12 days
Now For B and C
W=(rB+rC)tBC
tBC=15 days
where rC is the rate of C and tBC is the time taken by both B and C working together to finish the work.
We also know that
rA=2rC===>rC=rA/2 Substitute into ======>W=(rB+rC)tBC
to get
W=(rB+rA2)tBC
The time taken to finish the work by A alone is given by
tA=WrA
Equating
W=(rA+rB)tAB and W=(rB+rA2)tBC
you get
(rA+rB)tAB=W=(rB+rA2)tBC
Solve for rB to get
rB=1.5rA
Now use
W=(rA+rB)tAB=2.5rAtAB
Substitute the above into
tA=WrA=2.5×tAB=2.5×12=30 days
A + B = 12 days
B + C = 15 days
Efficiency - A/C = 2/1
Therefore one day work for -
A = 2u and C = 1u
Let the total work be 60u ( LCM of 12 and 15)
One day work for -
A + B = 5u - (1)
B + C = 4u - (2)
Putting the value of A=2u in eq. 1
B = 3u
Now no. of days taken by B to complete the work = 60 / 3 = 20 days
For A = 60 / 2 = 30 days
For C = 60 /1 = 60 days