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Machines A and B, working together, take t minutes to comple [#permalink]
 23 Feb 2013, 01:44
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Machines A and B, working together, take t minutes to complete a particular work. Machine A, working alone, takes 64 minutes more than t to complete the same work. Machine B, working alone, takes 25 minutes more than t to complete the same work. What is the ratio of the time taken by machine A to the time taken by machine B to complete this work? (A) 5:8 (B) 8:5 (C) 25:64 (D) 25:39 (E) 64:25
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Re: Machines A and B, working together, take t minutes [#permalink]
23 Feb 2013, 04:37
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This is a long problem, difficult to solve in 2 minutes. First, use the work problems formula: \frac{1}{t} = \frac{1}{t_a} + \frac{1}{t_b}Then, use the information on the problem statement: t_a = t+64 --> t_a = t+8^2t_b = t+25 --> t_b = t+5^2Now, substitute and solve: \frac{1}{t} = \frac{1}{(t+8^2)} + \frac{1}{(t+5^2)}\frac{1}{t} = \frac{(5^2+t+t+8^2)}{(t^2+5^2*t+8^2*t+8^2*5^2)}t^2+5^2*t+8^2*t+8^2*5^2 = 5^2*t + t^2 + t^2 + 8*t^2t^2=8^2*5^2t=8*5Finally, substitute to find the ratio \frac{t_a}{t_b}: \frac{t_a}{t_b}=\frac{(8*5+8^2)}{(8*5+5^2)}\frac{t_a}{t_b}=\frac{8*(5+8)}{5*(8+5)}\frac{t_a}{t_b}=\frac{8}{5}SOLTION: B
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Re: Machines A and B, working together, take t minutes to comple [#permalink]
23 Feb 2013, 11:10
skamal7 wrote: Machines A and B, working together, take t minutes to complete a particular work. Machine A, working alone, takes 64 minutes more than t to complete the same work. Machine B, working alone, takes 25 minutes more than t to complete the same work. What is the ratio of the time taken by machine A to the time taken by machine B to complete this work?
(A) 5:8
(B) 8:5
(C) 25:64
(D) 25:39
(E) 64:25 This has appeared at so many places so I keep this in my mind. total time taken by A and B together t ta (time taken by A alone) = t+ a tb (time taken by B alone) = t+ b then t*t = a*b This formula can be proved easily by applying the formula 1/t = 1/(t+a) + 1/(t+b) Total time taken together by A and B = sq root of product of extra time taken by A and B from t which means t*t = (25*64)
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Re: Machines A and B, working together, take t minutes to comple [#permalink]
23 Feb 2013, 11:16
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skamal7 wrote: Machines A and B, working together, take t minutes to complete a particular work. Machine A, working alone, takes 64 minutes more than t to complete the same work. Machine B, working alone, takes 25 minutes more than t to complete the same work. What is the ratio of the time taken by machine A to the time taken by machine B to complete this work?
(A) 5:8
(B) 8:5
(C) 25:64
(D) 25:39
(E) 64:25 Actually, there is no need for any calculation at all.... We know that A would take longer than B to complete the work. So, the only contenders are B & E. Now, "t" CANNOT be 0. So, the only option available is 8 : 5 P.S: When we add the same constant to both sides of a ratio, then the ratio "decreases" (if that is the right word) or a better term would be the ratio approaches 1 : 1 Illustration: 10 : 1 = 110 : 11 Adding 100 to both sides 110 : 101 = 110 : 101
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Re: Machines A and B, working together, take t minutes to comple [#permalink]
24 Feb 2013, 02:59
Quote: So, the only contenders are B & E. Now, "t" CANNOT be 0.
So, the only option available is 8 : 5 Hi Macfauz, I personally liked the way you approached the elimination strategy. Kudos! Can you please help me to understand why you chose B commenting t cannot be zero? Thanks a lot. Pritish
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Re: Machines A and B, working together, take t minutes to comple [#permalink]
24 Feb 2013, 05:06
pritish2301 wrote: Quote: So, the only contenders are B & E. Now, "t" CANNOT be 0.
So, the only option available is 8 : 5 Hi Macfauz, I personally liked the way you approached the elimination strategy. Kudos! Can you please help me to understand why you chose B commenting t cannot be zero? Thanks a lot. Pritish Time Taken By A : Time Taken By B = t + 64 : t + 25 If t is 0, the ratio will be 64:25. However, we do know that A & B cannot finish the work in literally no time. So "t" has to be greater than 0. So the answer we are looking for should be closer to 1:1 than 64:25 is and 8:5 is the only possible answer choice.
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Re: Machines A and B, working together, take t minutes to comple [#permalink]
24 Feb 2013, 05:08
Thank you very much!
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Re: Machines A and B, working together, take t minutes to comple
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24 Feb 2013, 05:08
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