4 sewing machines can sew shirts in the ratio of 1:2:3:5.

agree with leonidas

1/10 + 2/10 + 3/10= 3shirts/5hrs

machine 4 is fastest and it takes 2 hours to sew 5 shirts
we can say 120 /5 = 24 min for 1 shirt

machine 3: 120/3 = 40 min for 1 shirt

machine 2: 120/2 = 60 min for 1 shirt

machine 3: 120/1 = 12 min for 1 shirt


so total time taken by 1,2,3 machine will be

1/120 +1/60 +1/40 = 1+2+3/120 = 6/120 = 1/20

so it takes 1 hour - 60 minute for 20 shirts..will take 9 min. to sew 3 shirts

ha ha... i made some big mistake some where.. it can't be so easy

I got confused about this question on how we can assume that the sewing is in parallel. Is it realistic to have two machines or three machines producing one shirt? I thought the total time that three machines take in sewing 3 shirts will be the time taken by the slowest machine. However, in MGMAT's explanation they have considered all the machines producing shirts at the same time. Can someone please explain?

In work rate problems, many questions make you assume that work can be divided into infinitesimally small jobs and all machines work on these jobs to complete the work. Practically, I would think that one machine will sew one complete shirt. But since it is a work-rate problem, I would, unhappily, make the assumption that I don't have to worry about how the work will be divided. I just assume that each machine is working on the same shirt at its own rate.

"I thought the total time that three machines take in sewing 3 shirts will be the time taken by the slowest machine."

That would be my first thought too. But then, its not a work-rate problem anymore. Many questions specifically mention something like "All machines can work at the same time on a shirt" to make it clearer.

Combined speed of slower ones: Speed of fastest
1+2+3:5
6:5

5 times fast-> 2*3=6 hours
1 times fast-> 6*5 hours
6 times fast-> 6*5/6 hours= 5 hours

Ans: "5 hours"

fastest machine
1 shirt in 2hrs
5 shirts in 2*5 = 10 hrs

3 machines together make 6 shirts in 10 hrs (same time as the fastest takes to make 5 shirts)
time required to make 3 shirts = 5hrs

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