Question 34

P and Q together can complete some work in 30 days. Q and R together can do the same in 24 days. R and P together will take 20 days to complete it. If they all work together, in how many days will the job get done?

Solution

P+Q = 30 days

Q+R= 24 days

P+R = 20 days

Total work = lcm (30,24,20)= 240 days

(P+Q )'s effiency = $$240\div30$$ =8

(Q+R)'s effiency = $$240\div24$$ =10

(P+Q+R)'s efficiency = $$240\div 20$$ = 12

total efficiency = 2(Q+P+R)= 30

P+Q+R = 15

time taken = $$work\div effi $$

= $$240\div 15 $$

= 16 days

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