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Ratio and Proportion

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Ratio and Proportion

by karishma315 » Sun Jul 10, 2016 2:16 am
Please solve this question:

4 sewing machines can sew a shirt in the ratio of 1:2:3:5. Te fastest can sew a shirt in 2 hours. however , the fastest machine breaks . how long will it take the other three machines to sew a total of 3 shirts?

Thanks in advance.

regards
Karishma
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by GMATGuruNY » Sun Jul 10, 2016 3:01 am
karishma315 wrote:4 sewing machines can sew shirts in the ratio 1:2:3:5. the fastest can sew a shirt in 2 hours. however, the fastest machine breaks. how long will it take the other three machines to sew a total of 3 shirts?

Thanks in advance.

regards
Karishma
Fastest machine:
Let each shirt = the LCM of the values in the rate ratio = 1*2*3*5 = 30 units.
Since the fastest machine can sew one shirt in 2 hours, the rate for the fastest machine = w/t = 30/2 = 15 units per hour.

Other 3 machines:
Since the rate ratio for the 4 machines = 1:2:3:5 = 3:6:9:15, the rates for the other 3 machines are as follows:
3 units per hour
6 units per hour
9 units per hour.
Combined rate for the other 3 machines = 3+6+9 = 18 units per hour.

How long will it take the other three machines to sew a total of 3 shirts?
Since 1 shirt = 30 units, 3 shirts = 3*30 = 90 units.
At a combined rate of 18 units per hour, the time for the other 3 machines to produce 90 units = w/r = 90/18 = 5 hours.
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by OptimusPrep » Sun Jul 10, 2016 8:04 pm
karishma315 wrote:Please solve this question:

4 sewing machines can sew a shirt in the ratio of 1:2:3:5. Te fastest can sew a shirt in 2 hours. however , the fastest machine breaks . how long will it take the other three machines to sew a total of 3 shirts?

Thanks in advance.

regards
Karishma
Assume the rates to be x, 2x, 3x, 5x shirts every hour 0r 2x, 4x, 6x, 10x shirts every two hours
The fastest can sew 1 shirt in two hours

Hence 10x = 1
x = 0.1

Rates of machines = 0.1, 0,2, 0.3 and 0.5
The fastest machine breaks.

Total rate of other machines = 0.1 + 0.2 + 0.3 = 0.6

Total time taken to sew 3 machines = 3/0.6 = 5 hours
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