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# Harry and Ron can individually build a castle in 20 days and 30 days r

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e-GMAT Representative
Joined: 04 Jan 2015
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Harry and Ron can individually build a castle in 20 days and 30 days r  [#permalink]

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25 Apr 2017, 01:25
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Difficulty:

15% (low)

Question Stats:

82% (01:31) correct 18% (02:14) wrong based on 77 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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Saquib
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Harry and Ron can individually build a castle in 20 days and 30 days r  [#permalink]

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Updated on: 30 Apr 2017, 01:50
The official solution has been posted. Looking forward to a healthy discussion..
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Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
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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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Joined: 18 Jul 2016
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Re: Harry and Ron can individually build a castle in 20 days and 30 days r  [#permalink]

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25 Apr 2017, 02:10
1
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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Re: Harry and Ron can individually build a castle in 20 days and 30 days r  [#permalink]

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25 Apr 2017, 19:57
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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Re: Harry and Ron can individually build a castle in 20 days and 30 days r  [#permalink]

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30 Apr 2017, 01:48
1

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
.

Thanks,
Saquib
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Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

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Re: Harry and Ron can individually build a castle in 20 days and 30 days r &nbs [#permalink] 30 Apr 2017, 01:48
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