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EgmatQuantExpert
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A and B are two printing machines, which can complete a printing job t 28 Mar 2017, 10:39
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C
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25% (medium)

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82% (02:19) correct 18% (02:36) wrong based on 292 sessions

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Q. A and B are two printing machines, which can complete a printing job together in "T" hours. If A does the job alone, it takes 9 hours more than the usual time taken to complete the job together. And if B does the job alone, it takes 4 hours more than the usual time taken to complete the job together. Find the value of T.

    A. 3
    B. 5
    C. 6
    D. 16
    E. 18


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C
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A and B are two printing machines, which can complete a printing job t 31 Mar 2017, 04:08
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I wanted to discuss two ways to do this question and interestingly. Both the ways have used by the above two users. :D

Let me elaborate each of the methods.

    • As per the question –
      o Time taken by both A and B together = \(T\) hours.
      o Time taken by A alone = \((T + 9)\)hours.
      o Time taken by B alone = \((T + 4)\) hours


    • If we used the concept of one day’s work

      o A’s 1 day work would be = \(\frac{1}{(T+9)}\)……….(i)

      o B’s 1 day work would be = \(\frac{1}{(T+4)}\)……….(ii)

      o (A+B)’s 1 day work would be = \(\frac{1}{T}\)………(iii)

    • And we can very easily say that (i) + (ii) = (iii)

      o Thus, \(\frac{1}{(T+9)} + \frac{1}{(T+4)} = \frac{1}{T}\)

    • Now one might be tempted to use the options. But if you simplify, you will notice that you can get the answer very quickly.

    • Simplifying

      o \([(T+4) + (T+9)]*T = (T+4) * (T+9)\)

      o 2\(T^2 + 13T = T^2 + 13T + 36\)

      o \(T^2 = 36\)

      o Hence \(T = 6\) hours.

    • And the correct answer is Option C


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A and B are two printing machines, which can complete a printing job t Updated on: 31 Mar 2017, 04:24
Originally posted by EgmatQuantExpert on 28 Mar 2017, 10:40.
Last edited by EgmatQuantExpert on 31 Mar 2017, 04:24, edited 1 time in total.
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The official solution has been posted. Looking forward to a healthy discussion..:)
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A and B are two printing machines, which can complete a printing job t 28 Mar 2017, 21:38
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answer is C.
Rate A/Rate B = 9/T=T/4 =>T=6
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A and B are two printing machines, which can complete a printing job t 28 Mar 2017, 22:47
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1/(9+t) +1/(4+t)=1/t

substituting t =6 from the options satisfies the equation hence t=6.
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A and B are two printing machines, which can complete a printing job t 31 Mar 2017, 04:23
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The second is a bit more conceptually appealing.

    • When A and B work together they take \(T\) hours.

    • This means that A used to work for \(T\) hours and B also used to work for \(T\) hours.

    • But when A works alone, A takes \((T+9)\) hours.

      o Now think, why does A take \(9\) hours extra?

      o Of course, to do the work which B was doing, when they were working together.

      o And how much time was B taking to do the work, which A is doing in \(9\) hours?

      o Focus on the bold portion above, B used to take \(T\) hours, to do what A is doing in \(9\) hours.

         Since, we know efficiency and time are inversely proportional we can write –

         \(\frac{E_A}{E_B}\) = \(\frac{(Time taken by B)}{(Time taken by A)}\)

         \(\frac{E_A}{E_B} = \frac{T}{9}\)…..(ii)

    • Similary when B works alone, B takes \((T+4)\) hours.

      o Now think, why does B take \(4\) extra hours?

      o Because in those 4 hours, B will do the work which A used to do in \(T\) hours when they were working together.

         Since, we know efficiency and time are inversely proportional we can write –

         \(\frac{E_A}{E_B}\) = \(\frac{(Time taken by B)}{(Time taken by A)}\)

         \(\frac{E_A}{E_B} = \frac{4}{T}\)…..(ii)


    • Equating Equation (i) and (ii), we get

      o \(\frac{T}{9} = \frac{4}{T}\)

      o \(T^2 = 9 *4\)

      o \(T = 6\) hours


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A and B are two printing machines, which can complete a printing job t 11 Aug 2024, 08:26
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