P can do a job in 3 days , q can do 3 times that job in 8 days and r can do 5 times that job in 12 days. if all of them work together , they will finish one job in ?
Answers
Answer:
P one day work = 1/3
Q one day work = 3/8
R one day work = 5/12
(P+Q+R) one day work = 1/3+ 3/8+ 5/12
= 9/8
(P+Q+R) will complete the work in 8/9 days
The work will be done in 8/9 day , if they work together.
P can do a job in 3 days, q can do 3 times that job in 8 days and r can do 5 times that job in 12 days.
If all of them work together, they will finish the job in ..
we have to find the efficiency of p , q and r so that we can find how many days they complete the work together.
using formula,
M₁D₁/W₁ = M₂D₂/W₂ = M₃D₃/W₃
M₁ = p, M₂ = q and M₃ = r
D₁ = 3 days , D₂ = 8 days and D₃ = 12 days
W₁ = 1 , W₂ = 3 and W₃ = 5.
∴ (p × 3)/1 = (q × 8)/3 = (r × 12)/5
⇒p × 3 = q × 8/3 = r × 12/5
⇒p × 45 = q × 40 = r × 36
⇒p/8 = q/9 = r/10
so, the ratio of their efficiencies = 8 : 9 : 10
now they work together to do one job,
so, total units of job = efficiency of p × no of days
no of days × sum of efficiencies of p, q and r = 8 × 3 = 24 units
⇒no of days × (8 + 9 + 10) = 24 units
⇒no of days = 24/27 = 8/9 day.