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# Chris’s plot of land for his garage is 1/4 the size of his plot of lan

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Chris’s plot of land for his garage is 1/4 the size of his plot of lan  [#permalink]

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22 Jan 2019, 10:07
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45% (medium)

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69% (02:24) correct 31% (02:38) wrong based on 54 sessions

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Chris’s plot of land for his garage is $$\frac{1}{4}$$ the size of his plot of land for his house. If Chris plans to sell $$\frac{1}{2}$$ of the plot of land for his house and $$\frac{3}{4}$$ of his plot of land for his garage, what fraction of his land will remain unsold?

A) $$\frac{1}{4}$$

B) $$\frac{1}{3}$$

C) $$\frac{9}{20}$$

D) $$\frac{1}{2}$$

E) $$\frac{11}{20}$$

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Re: Chris’s plot of land for his garage is 1/4 the size of his plot of lan  [#permalink]

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22 Jan 2019, 11:00
total plot size (house + garage) = 1+1/4 = 5/4
Unsold house plot = 1/2
Unsold garage plot = 1/4of(1/4 of house plot) = 1/16
total unsold = 9/16
fraction of unsold plot = (9/16)*(4/5) = 9/20

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Chris’s plot of land for his garage is 1/4 the size of his plot of lan  [#permalink]

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22 Jan 2019, 11:20
CAMANISHPARMAR wrote:
Chris’s plot of land for his garage is $$\frac{1}{4}$$ the size of his plot of land for his house. If Chris plans to sell $$\frac{1}{2}$$ of the plot of land for his house and $$\frac{3}{4}$$ of his plot of land for his garage, what fraction of his land will remain unsold?

A) $$\frac{1}{4}$$

B) $$\frac{1}{3}$$

C) $$\frac{9}{20}$$

D) $$\frac{1}{2}$$

E) $$\frac{11}{20}$$

Let the plot of land for the house be 16 units

So, Plot of land for Garage is 4 units

Total plot of land for garage and House is 20 units

Chris sells 1/2 of the plot of land of house So he sells 8 units and is left with 8 units of land for house

And, He sells 3/4thplot of land of garafe , so he sells 3 units and is left with 1 unit..

Thus, Part of land left unsold is ( 8 + 1 )/20 = 9/20, Thus Answer must be (C) $$\frac{9}{20}$$
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Re: Chris’s plot of land for his garage is 1/4 the size of his plot of lan  [#permalink]

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09 Apr 2019, 06:14
skhemani wrote:
total plot size (house + garage) = 1+1/4 = 5/4
Unsold house plot = 1/2
Unsold garage plot = 1/4of(1/4 of house plot) = 1/16
total unsold = 9/16
fraction of unsold plot = (9/16)*(4/5) = 9/20

why did you flip the total house plot from 5/4 to 4/5?
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Re: Chris’s plot of land for his garage is 1/4 the size of his plot of lan  [#permalink]

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10 Apr 2019, 18:01
CAMANISHPARMAR wrote:
Chris’s plot of land for his garage is $$\frac{1}{4}$$ the size of his plot of land for his house. If Chris plans to sell $$\frac{1}{2}$$ of the plot of land for his house and $$\frac{3}{4}$$ of his plot of land for his garage, what fraction of his land will remain unsold?

A) $$\frac{1}{4}$$

B) $$\frac{1}{3}$$

C) $$\frac{9}{20}$$

D) $$\frac{1}{2}$$

E) $$\frac{11}{20}$$

If we let the plot of land for the house = 80 acres and the plot of land for the garage = 20 acres, then the total land = 100 acres.

So Chris sells 1/2 x 80 = 40 acres of the plot of land for his house and 3/4 x 20 = 15 acres of the plot of land for his garage, for a total of 55 acres, or 55/100 = 11/20, of the plot of land.

Therefore, the fraction of his land that is unsold is 1 - 11/20 = 9/20.

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Re: Chris’s plot of land for his garage is 1/4 the size of his plot of lan   [#permalink] 10 Apr 2019, 18:01
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