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# A farmer can plow the corn field in 12 days. A farmer can plow the cor

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Intern
Joined: 07 Dec 2016
Posts: 38
A farmer can plow the corn field in 12 days. A farmer can plow the cor  [#permalink]

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15 Apr 2017, 08:38
2
5
00:00

Difficulty:

25% (medium)

Question Stats:

78% (02:06) correct 22% (02:21) wrong based on 173 sessions

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A farmer can plow the corn field in 12 days. After working for 5 days, his son joins him and together they finish plowing the field in 4 days. How many days would it take the son to plow the corn field alone?

A) 9 days
B) 10 days
C) 11 days
D) 13 days
E) 16 days

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Math Expert
Joined: 02 Aug 2009
Posts: 7763
Re: A farmer can plow the corn field in 12 days. A farmer can plow the cor  [#permalink]

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15 Apr 2017, 09:18
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amathews wrote:
A farmer can plow the corn field in 12 days. After working for 5 days, his son joins him and together they finish plowing the field in 4 days. How many days would it take the son to plow the corn field alone?

A) 9 days
B) 10 days
C) 11 days
D) 13 days
E) 16 days

proper method

Farmer does work in 12 days so his ONE day work= 1/12..
work left after 5 days = 1-5/12=7/12..

If 7/12 of work is finished in 4 days, entire work could be finished by both = 4*12/7=48/7..
Thus one day work of both combined=7/48..

So one day work of son = $$\frac{7}{48}-\frac{1}{12}=\frac{7-4}{48}=\frac{1}{16}$$..
Therefore son can complete the work in 16 days..

Faster and logical method
Farmer works for 5+4 or 9 days...
If he completes entire work in 12 days, he will finish 9/12 or 3/4 in 9 days..

Remaining work, 1-3/4=1/4, is done by son in 4 days..
So if son does 1/4 in 4 days, he will complete the work in 4*4=16 days.

E
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Director
Joined: 05 Mar 2015
Posts: 998
Re: A farmer can plow the corn field in 12 days. A farmer can plow the cor  [#permalink]

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15 Apr 2017, 09:23
2
amathews wrote:
A farmer can plow the corn field in 12 days. After working for 5 days, his son joins him and together they finish plowing the field in 4 days. How many days would it take the son to plow the corn field alone?

A) 9 days
B) 10 days
C) 11 days
D) 13 days
E) 16 days

work done by farmer in 5 days = 5/12
work done by farmer in next 4 days = 4/12
Let rate of son = 1/a , or son complete the work in a days
then work done by son in 4 days (along farmer) = 4/a

then as per stem

5/12 + 4/12 + 4/a = 1

thus a = 16 days

Ans E
VP
Joined: 07 Dec 2014
Posts: 1211
A farmer can plow the corn field in 12 days. A farmer can plow the cor  [#permalink]

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15 Apr 2017, 10:02
amathews wrote:
A farmer can plow the corn field in 12 days. After working for 5 days, his son joins him and together they finish plowing the field in 4 days. How many days would it take the son to plow the corn field alone?

A) 9 days
B) 10 days
C) 11 days
D) 13 days
E) 16 days

let r=son's rate
4(1/12+r)=7/12
r=1/16
son's time=16 days
E
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A farmer can plow the corn field in 12 days. A farmer can plow the cor  [#permalink]

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26 Apr 2017, 22:08
1
1
Farmer's rate of work per day is -$$\frac{1}{12}$$

In all, farmer worked for 9 days, so the amount of work
Farmer did -$$\frac{9}{12}$$
So his son did - $$\frac{3}{12}$$ = 25% of work in 4 days. So for him to complete the work alone would take 16 days.
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Re: A farmer can plow the corn field in 12 days. A farmer can plow the cor  [#permalink]

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29 Oct 2018, 03:50
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Re: A farmer can plow the corn field in 12 days. A farmer can plow the cor   [#permalink] 29 Oct 2018, 03:50
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