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EgmatQuantExpert
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Harry and Ron can individually build a castle in 20 days and 30 days r 25 Apr 2017, 01:25
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87% (01:43) correct 13% (02:26) wrong based on 214 sessions

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Q. Harry and Ron can individually build a castle in 20 days and 30 days respectively. Both work together for 6 days, after which Harry and Ron got tired and quit. Hermione decided to complete the castle and worked for 5 days alone to complete the remaining work. Had Hermione worked alone, in how many days would she have built the whole castle?

    a. 5 days
    b. 10 days
    c. 15 days
    d. 20 days
    e. 30 days

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Harry and Ron can individually build a castle in 20 days and 30 days r Updated on: 30 Apr 2017, 01:50
Originally posted by EgmatQuantExpert on 25 Apr 2017, 01:25.
Last edited by EgmatQuantExpert on 30 Apr 2017, 01:50, 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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Harry and Ron can individually build a castle in 20 days and 30 days r 25 Apr 2017, 02:10
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rate of work for
Harry = 1/20
Ron = 1/30

when working together, rate = 1/20 + 1/30 = 5/60 = 1/12
worked for 6 days means they completed 1/12 * 6 work = 1/2

Hermione works for 5 days to complete 1/2 work
so rate of hermione's work = (1/2)/5 = 1/10
hence she can complete the castle in 10 days
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Harry and Ron can individually build a castle in 20 days and 30 days r 25 Apr 2017, 19:57
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Harry's 6 day work = 6/20
Ron's 6 day work = 6/30
together theri work = 6/20 + 6/30 = 1/2
Remaining work is 1/2 which Hermione completed in 5 days
so the 1 day work by Hermione alone is (1/2)/5 = 1/10
Total days = 10
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Harry and Ron can individually build a castle in 20 days and 30 days r 30 Apr 2017, 01:48
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Solution




    • We are given:

      o Time taken by Harry to build the castle \(= 20\) \(days\).
      o Time taken by Ron to build the castle \(= 30\) \(days\).

    • Let us assume the work to be \(60\) \(units\) (LCM of 20 and 30)

      o Efficiency of Harry \(= \frac{60}{20} = 3\) units/day
      o Efficiency of Ron \(= \frac{60}{30} = 2\) unit/day
    • If they work together they can build the castle in \(= \frac{60}{(2+3)} = 10\) days.

      o But they are working for only \(5\) \(days\).
      o Hence they will complete only half of the work which is \(30\) \(units\).

    • The remaining half (\(30 units\)) of the work is done by Hemione in \(5\) \(days\).
    • Thus, Hermione can complete the total work in \(5*2 = 10\) \(days\).
    • And the correct answer is Option B
.


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Harry and Ron can individually build a castle in 20 days and 30 days r 30 Dec 2023, 04:51
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