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# There are 8 fields of exactly the same size that are to be plowed by 7

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Math Expert
Joined: 02 Sep 2009
Posts: 56257
There are 8 fields of exactly the same size that are to be plowed by 7  [#permalink]

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03 Jan 2019, 12:45
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Difficulty:

15% (low)

Question Stats:

86% (02:07) correct 14% (01:48) wrong based on 82 sessions

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There are 8 fields of exactly the same size that are to be plowed by 7 farmers who work at identical rates. If it takes 5 hours for 4 of the farmers to plow the first 2 fields, how many hours will it take the remaining 3 farmers to plow the remaining 6 fields?

A. 18
B. 19
C. 20
D. 21
E. 22

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Joined: 04 Jan 2015
Posts: 2943
There are 8 fields of exactly the same size that are to be plowed by 7  [#permalink]

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04 Jan 2019, 03:22
4
1

Solution

Given:
• Number of fields to be ploughed = 8
• All farmers work at the same rate
• 4 farmers take 5 hours to plough the first 2 fields

To find:
• The time taken in hours, by the remaining 3 farmers to plough the rest 6 fields

Approach and Working:
• 4 farmers take $$\frac{5}{2} = 2.5$$hours to plough 1 field
• 1 farmer takes 2.5*4 = 10 hours to plough 1 field
• 1 farmer takes 10*6 = 60 hours to plough 6 fields

Therefore, 3 farmers take $$\frac{60}{3} = 20$$ hours to plough 6 fields

Hence, the correct answer is Option C

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Re: There are 8 fields of exactly the same size that are to be plowed by 7  [#permalink]

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03 Jan 2019, 20:07
Bunuel wrote:
There are 8 fields of exactly the same size that are to be plowed by 7 farmers who work at identical rates. If it takes 5 hours for 4 of the farmers to plow the first 2 fields, how many hours will it take the remaining 3 farmers to plow the remaining 6 fields?

A. 18
B. 19
C. 20
D. 21
E. 22

It took 5 hours for 4 of the farmers to plow the first 2 fields.

Let x be the number of hours for the remaining 3 farmers to plow the remaining 6 fields.

Equating rates,

$$\frac{5*4}{2}=\frac{3*x}{6}$$

Solve for x,

x=20

IMO, Option C
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Posts: 9446
Location: Pune, India
Re: There are 8 fields of exactly the same size that are to be plowed by 7  [#permalink]

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04 Jan 2019, 01:02
Bunuel wrote:
There are 8 fields of exactly the same size that are to be plowed by 7 farmers who work at identical rates. If it takes 5 hours for 4 of the farmers to plow the first 2 fields, how many hours will it take the remaining 3 farmers to plow the remaining 6 fields?

A. 18
B. 19
C. 20
D. 21
E. 22

Using the methodology discussed in this post: https://www.veritasprep.com/blog/2015/1 ... made-easy/

We get:

2 fields .......... 4 farmers .......... 5 hours
6 fields .......... 3 farmers .......... ?? hours

No of hrs = 5 * (6/2) * (4/3) = 20 hrs

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Re: There are 8 fields of exactly the same size that are to be plowed by 7  [#permalink]

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06 Jan 2019, 06:03
Bunuel wrote:
There are 8 fields of exactly the same size that are to be plowed by 7 farmers who work at identical rates. If it takes 5 hours for 4 of the farmers to plow the first 2 fields, how many hours will it take the remaining 3 farmers to plow the remaining 6 fields?

A. 18
B. 19
C. 20
D. 21
E. 22

time per farmer to plow one field

5*4/2 = 10 hrs per field
so 3 farmers will take 6 * 10 = 60 /3 = 20 hrs
IMO C
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Re: There are 8 fields of exactly the same size that are to be plowed by 7  [#permalink]

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06 Jan 2019, 18:49
Bunuel wrote:
There are 8 fields of exactly the same size that are to be plowed by 7 farmers who work at identical rates. If it takes 5 hours for 4 of the farmers to plow the first 2 fields, how many hours will it take the remaining 3 farmers to plow the remaining 6 fields?

A. 18
B. 19
C. 20
D. 21
E. 22

This kinda question can be solved easily by using the following formula:

No. of workers * Rate * Time = Work

4 * Rate * 5 = 2

Rate = 2/20 = 1/10.

Now we will substitute this rate to the same formula for different values.

No. of workers * Rate * Time = Work

3 * 1/10 * Time = 6

Time = 60/3

Time = 20 hrs.

Re: There are 8 fields of exactly the same size that are to be plowed by 7   [#permalink] 06 Jan 2019, 18:49
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