Anthony, Brian and Chris are hired for a job. If Anthony and Brian are working together they will finish the job in minutes. If Anthony and Chris are working together they will finish the job in minutes. If Brian and Chris are working together, they will finish the job in hour. If the Chris is working alone, how long will it take him to finish the job
Answers
Correct Question :- Anthony, Brian and Chris are hired for a job. If Anthony and Brian are working together they will finish the job in 36 minutes. If Anthony and Chris are working together they will finish the job in 45 minutes. If Brian and Chris are working together, they will finish the job in 1 hour. If the Chris is working alone, how long will it take him to finish the job ?
Solution :-
LCM of (36,45,60) = 180 units = Let total work.
so,
→ Efficiency of (Anthony + Brian) = Total work / Time taken = 180/36 = 5 units/Min . --------------- Eqn.(1)
similarly,
→ Efficiency of (Anthony + Chris) = Total work / Time taken = 180/45 = 4 units/Min . --------------- Eqn.(2)
and,
→ Efficiency of (Brian + Chris) = Total work / Time taken = 180/60 = 3 units/Min . --------------- Eqn.(3)
adding all three equations we get,
→ (Anthony + Brian) + (Anthony + Chris) + (Brian + Chris) = 5 + 4 + 3
→ 2(Anthony + Brian + Chris) = 12
→ (Anthony + Brian + Chris) = 6 units / Min. ------------- Eqn.(4)
then, subtracting Eqn.(1) from Eqn.(4) we get,
→ (Anthony + Brian + Chris) - (Anthony + Brian) = 6 - 5
→ Chris = 1 unit / Min.
therefore,
→ Time taken by chris to finish the job if working alone = (Total work)/Efficiency = 180/1 = 180 Min. = 3 hours. (Ans.)
Hence, Chris alone can finish the job in 3 Hours .
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Answer:
Chris alone can finish the job in 3 Hours .
Step-by-step explanation:
the total time taken by Chris is 3 hours