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Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at

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Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at  [#permalink]

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New post 23 Jan 2019, 09:38
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Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at m% profit. If Mr. A bought it for $ 12000, what was its cost price for Mr. C?

I. m+n+mn/100=44
II. n+m=0.40
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Re: Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at  [#permalink]

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New post 23 Jan 2019, 10:17
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akurathi12 wrote:
Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at m% profit. If Mr. A bought it for $ 12000, what was its cost price for Mr. C?

I. m+n+mn/100=44
II. n+m=0.40


from the given:
\(B - A\) = \(\frac{n}{100} A\),
\(B\) = \(A(\frac{n}{100} + 1)\)

\(C - B\) = \(\frac{m}{100} B\),
\(C\) = \(B(\frac{m}{100} + 1)\) = \(A(\frac{n}{100} + 1)(\frac{m}{100} + 1)\)

if A = 12000,
\(C\) = \(12000*(\frac{n}{100} + 1)(\frac{m}{100} + 1)\)
\(C\) = \(12000*(\frac{n}{100} + \frac{m}{100} + \frac{nm}{10000} + 1)\)

statement I: \(m+n+\frac{mn}{100}=44\)

\(\frac{n}{100} + \frac{m}{100} + \frac{nm}{10000} = \frac{44}{100}\)
\(C\) = \(12000*(\frac{44}{100}+ 1)\) = \(120*144\)(#sufficient)

statement II: \(n+m=0.40\)
2 variables with one equation , (#insufficient)

so A is the answer
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Re: Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at  [#permalink]

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New post 23 Jan 2019, 10:18
akurathi12 wrote:
Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at m% profit. If Mr. A bought it for $ 12000, what was its cost price for Mr. C?

I. m+n+mn/100=44
II. n+m=0.40


Statement 1)
So what m+n+mn/100=44 denotes = successive percentage change

Cost of C will be 44% of 12000 + 12000

Sufficient

Statement 2)
This is not all sufficient, as the addition of profit percentages, can be in any order.

Answer A
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Re: Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at  [#permalink]

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New post 23 Jan 2019, 19:09
KanishkM wrote:
akurathi12 wrote:
Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at m% profit. If Mr. A bought it for $ 12000, what was its cost price for Mr. C?

I. m+n+mn/100=44
II. n+m=0.40


Statement 1)
So what m+n+mn/100=44 denotes = successive percentage change

Cost of C will be 44% of 12000 + 12000

Sufficient

Statement 2)
This is not all sufficient, as the addition of profit percentages, can be in any order.

Answer A


Hi, I didn't understand the statement 1. can you please explain elaborately.
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Re: Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at  [#permalink]

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New post 23 Jan 2019, 19:48
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akurathi12 wrote:

Hi, I didn't understand the statement 1. can you please explain elaborately.


Sure.

Whenever there is a successive change, this means that for a single commodity when in a succession(like in the below example) percentage is increased/decreased we can use the inline formula( learning how its derived i think will not be that fruitful)

a + b + (ab)/100

here a, b based on the question can be the profit % or the loss %.

Since they both are +ive in the question, we can use them as it is,but if one % was a loss then we will take the sign as negative

a = 10 % profit
b = 10 % loss

Successive percentage = 10 -10 -100/100 = -1%

Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at m% profit. If Mr. A bought it for $ 12000, what was its cost price for Mr. C?

So what m+n+mn/100=44 denotes = successive percentage change

Cost of C will be 44% of 12000 + 12000 or 144 % of 12000)

Sufficient.

Let me know if this helps you.
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
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Re: Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at   [#permalink] 23 Jan 2019, 19:48
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