superpus07 wrote:
Machine A currently takes x hours to complete a certain job. Machine B currently takes y hours to complete the same job. If x=4y, by what percent will x have to decrease so that A and B together can complete the job in 3y/8 hours ?
A. 15%
B. 25%
C. 30%
D. 62,5%
E. 85%
We can assume a suitable value of y (and hence x) and calculate the answer:
Let y = 8 hours => Time taken by B to complete the work = 8 hours
=> x = 32 hours => Time taken by A to complete the work = 32 hours
Note: At the above rates, fraction of work done by A and B in 1 hour = 1/8 + 1/32 = 5/32=> Time taken by A and B together to complete the work = 32/5 hoursHowever, we need to complete the work in 3y/8 = 3 hours
Thus, in each hour, A and B should do 1/3 rd of the work
=> Work done by A in 1 hour (after the value of x is changed) = 1/3 - 1/8 = 5/24
=> Time (new) taken by A to complete the work = 24/5 = 4.8 hours
The question asks: "what percent will x have to decrease"
Thus, it is asking about the percent change in time
=> Required percent = (32 - 4.8)/32 * 100 = 85%
Answer E
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