diebeatsthegmat wrote:T can work alone and will finish job in 6 hours, P & J can do the same independently in 3 and 2 hours each. T starts working alone and after 1 hour P joins, both of them work for another 1 hour. After that J joins them and they finish the job together. What was fraction of job done by T????
1) 1/9
2) 1/6
3) 1/3
4) 7/18
5) 4/9
Let job = 6 units.
Rate for T = w/t = 6/6 = 1 unit per hour.
Rate for P = w/t = 6/3 = 2 units per hour.
Rate for J = w/t = 6/2 = 3 units per hour.
Work completed by T in 1 hour = r*t = 1*1 = 1 unit.
Combined rate for T and P = 1+2 = 3 units per hour.
Work completed by T+P in 1 hour = r*t = 3*1 = 3 units.
Remaining work = 6-1-3 = 2 units.
Combined rate for T,P and J = 1+2+3 = 6 units per hour.
Time to produce the remaining 2 units = w/r = 2/6 = 1/3 of an hour.
Total time for T = 1+1+(1/3) = 7/3 hours.
Work produced by T = r*t = 1*(7/3) = 7/3 units.
Fraction of work produced by T = (7/3)/6 = 7/18.
The correct answer is
D.
If the OA is
B, then the question must be asking for the fraction of the work produced by J.
Since J works only for 1/3 of an hour, work produced by J = r*t = 3*(1/3) = 1 unit.
Fraction of work produced by J = 1/6.
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