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If 17 labourers can dig a ditch 20 m long in 18 days, working 8 hours

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Bunuel
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If 17 labourers can dig a ditch 20 m long in 18 days, working 8 hours [#permalink] New post   28 Dec 2019, 01:37
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If 17 labourers can dig a ditch 20 m long in 18 days, working 8 hours a day, how many minimum number of more labourers should be engaged to dig a similar ditch 39 m long in maximum of 6 days, each labourer working 9 hours per day.

A. 89
B. 84 3
C. 78
D. 72
E. 68
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Re: If 17 labourers can dig a ditch 20 m long in 18 days, working 8 hours [#permalink] New post   28 Dec 2019, 06:35
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Bunuel wrote:
If 17 labourers can dig a ditch 20 m long in 18 days, working 8 hours a day, how many minimum number of more labourers should be engaged to dig a similar ditch 39 m long in maximum of 6 days, each labourer working 9 hours per day.

A. 89
B. 84 3
C. 78
D. 72
E. 68

use
m1*t1/w1 = m2*t2/w2
solve for m2 = ~ 81.4
and additional labor required= 88.4-17 ; ~ 72
IMO D
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Re: If 17 labourers can dig a ditch 20 m long in 18 days, working 8 hours [#permalink] New post   08 Jan 2020, 04:27
Solution:
Digging 20 m long in 18x8 hours by 17 lobourers
1 1 17x18x8/20
39 6x9 17x18x8x39/20x6x9
= 89
Number of more labor = 89-17 = 72(D)
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Re: If 17 labourers can dig a ditch 20 m long in 18 days, working 8 hours [#permalink] New post   10 Jan 2020, 07:34
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Bunuel wrote:
If 17 labourers can dig a ditch 20 m long in 18 days, working 8 hours a day, how many minimum number of more labourers should be engaged to dig a similar ditch 39 m long in maximum of 6 days, each labourer working 9 hours per day.

A. 89
B. 84 3
C. 78
D. 72
E. 68


The hourly rate of 1 labourer is 20 / (17 x 18 x 8). Let n = the number of labourers needed to dig a 39 m long ditch in 6 days with each labourer working 9 hours per day. We can create the equation:

20 / (17 x 18 x 8) = 39 / (n x 6 x 9)

20(n x 6 x 9) = 39(17 x 18 x 8)

20 x 54 x n = 3 x 13 x 17 x 18 x 8

20n = 13 x 17 x 8

n = 13 x 17 x 8 / 20 = 88.4

However, we can’t have the number of labourers as a decimal number, and since the job should take a maximum of 6 days, we need more than “88.4” labourers, so 89 labourers will do. Since we already have 17 labourers, we will need an additional 89 - 17 = 72 labourers.

Answer: D
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Re: If 17 labourers can dig a ditch 20 m long in 18 days, working 8 hours [#permalink]
10 Jan 2020, 07:34
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