X can do a work in 3 days, Y does three times the same work in 8 days, and Z does five times the same work in 12 days. If they have to work together for 6 hours in a day, then in how much time can they complete the work?
Answers
you can take this example similar to your question:
If the total efforts needed to complete the job is A. Therefore capacity of X to work in one day is A/5..
of B = 2A/15 and
of C = 3A/7
total work done by all three together in one day = A/5+2A/15+3A/7= 16A/21
now question asks for the time taken if three work together for 8 hrs/day.
let us assume that the capacities given in the question are for 24 hrs working( though surprising)
therefore the desired answer = (21/16)* 24/8= 63/16 days.
Given:
X can complete the work in 3 days.
Y can do three times the same work in 8 days.
Z does five times the same work in 12 days.
Working hours per day = 6 hours
Formula used:
Efficiency = Total work/Total Time
Calculations:
Let the total work be 1 unit.
Time to complete 1 unit by X alone = 3 × 6 = 18 hours
Time to complete the 3 units by Y alone = 8 × 6 = 48 hours
Time to complete the 1 unit by Y alone = 48/3 = 16 hours
Time to complete the 5 units by Z alone = 12 × 6 = 72 hours
Time to complete the 1 unit by Z alone = 72/5 hours
Efficiency of X = 1/18 units/hour
Efficiency of Y = 1/16 units/hour
Efficiency of Z = 5/72 units/hour
Combined efficiency of X, Y and Z = (1/18) + (1/16) + (5/72)
⇒ (8 + 9 + 10)/144
⇒ 27/144 units/hour
Time to complete total work by X, Y and Z together
⇒ 1/(27/144)
⇒ 144/27 hours
⇒ 5 hours 20 minutes
∴ They can complete the work in 5 hours 20 minutes.