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A trader has lost 15% on a $10,000 investment. He is going to buy a st

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A trader has lost 15% on a $10,000 investment. He is going to buy a st [#permalink]

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New post 19 Mar 2017, 06:11
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A trader has lost 15% on a $10,000 investment. He is going to buy a stock that is guaranteed a 12% gain. How much should he invest in this stock so that the net gain for the entire portfolio is 4%?

A. $23,750
B. $15,833
C. $13,750
D. $10,700
E. $10,000
[Reveal] Spoiler: OA

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A trader has lost 15% on a $10,000 investment. He is going to buy a st [#permalink]

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New post 19 Mar 2017, 06:23
Bunuel wrote:
A trader has lost 15% on a $10,000 investment. He is going to buy a stock that is guaranteed a 12% gain. How much should he invest in this stock so that the net gain for the entire portfolio is 4%?

A. $23,750
B. $15,833
C. $13,750
D. $10,700
E. $10,000


let x be the amount that must be invested

12x/100 - (15/100)*10000 = (4/100)*(10000+x)
12x/100 - 1500 = 400 + 4x/100
12x - 4x = 190000
x = 23,750
Hence option A is correct
Hit Kudos if you liked it 8-)

Last edited by 0akshay0 on 19 Mar 2017, 08:04, edited 1 time in total.
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Re: A trader has lost 15% on a $10,000 investment. He is going to buy a st [#permalink]

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New post 19 Mar 2017, 06:49
let x be the amount that must be invested

(-0,15*10000+0,12*x)/(10000+x)=0,04 => (-1500+0,12x)/(10000+x)=0,04 =>-1500+0,12x=400+0,04x =>0,08x=1900 => x=23750
Answer is A
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A trader has lost 15% on a $10,000 investment. He is going to buy a st [#permalink]

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New post 19 Mar 2017, 07:07
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kwindi wrote:
let x be the amount that must be invested

(-0,15*10000+0,12*x)/(10000+x)=0,04 => (-1500+0,12x)/(10000+x)=0,04 =>-1500+0,12x=400+0,04x =>0,08x=1900 => x=23750
Answer is A


since the trader lost 15% on 10000. He was left with 8500.

now 12% of x = 0.12 * 23750 (according to your answer) = 2850.... so 2850 + 8500 = 11350

(11350-10000)/10000 = 1350/10000 = 13.5% and not 4% net gain.

hope its clear :)
Kudos if you liked it 8-)
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Re: A trader has lost 15% on a $10,000 investment. He is going to buy a st [#permalink]

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New post 19 Mar 2017, 07:22
0akshay0 wrote:
kwindi wrote:
let x be the amount that must be invested

(-0,15*10000+0,12*x)/(10000+x)=0,04 => (-1500+0,12x)/(10000+x)=0,04 =>-1500+0,12x=400+0,04x =>0,08x=1900 => x=23750
Answer is A


since the trader lost 15% on 10000. He was left with 8500.

now 12% of x = 0.12 * 23750 (according to your answer) = 2850.... so 2850 + 8500 = 11350

(11350-10000)/10000 = 1350/10000 = 13.5% and not 4% net gain.

hope its clear :)
Kudos if you liked it 8-)


The portfolio consists of 2 assets: one in which we invested 10000 and the second one in which we invest x. Therefore, the net gain is 0,12*x-0,15*10000=0,12x-1500. Meaning that the return is (0,12x-1500)/(total investment=10000+x)=0,04
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Re: A trader has lost 15% on a $10,000 investment. He is going to buy a st [#permalink]

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New post 19 Mar 2017, 07:46
A 23750 ✓

-1500 + 0.12x = 0.04x ( 10000+x)

Where x is the amount he decides to invest in stock that has return of 12%



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Re: A trader has lost 15% on a $10,000 investment. He is going to buy a st [#permalink]

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New post 19 Mar 2017, 07:51
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Let the amount to be invested be x. So,

12% of x - 1500 = 4% of (10000 + x){the amount invested at 12% needs to make up for the $1500 loss to give an overall 4% gain}

12% of x -1500 = 400 + 4% of x
12% of x - 4% of x = 1900
8% of x = 1900

x = 1900 *100/8
x = 23750
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A trader has lost 15% on a $10,000 investment. He is going to buy a st [#permalink]

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New post 19 Mar 2017, 08:24
kwindi wrote:
0akshay0 wrote:
kwindi wrote:
let x be the amount that must be invested

(-0,15*10000+0,12*x)/(10000+x)=0,04 => (-1500+0,12x)/(10000+x)=0,04 =>-1500+0,12x=400+0,04x =>0,08x=1900 => x=23750
Answer is A


since the trader lost 15% on 10000. He was left with 8500.

now 12% of x = 0.12 * 23750 (according to your answer) = 2850.... so 2850 + 8500 = 11350

(11350-10000)/10000 = 1350/10000 = 13.5% and not 4% net gain.

hope its clear :)
Kudos if you liked it 8-)


The portfolio consists of 2 assets: one in which we invested 10000 and the second one in which we invest x. Therefore, the net gain is 0,12*x-0,15*10000=0,12x-1500. Meaning that the return is (0,12x-1500)/(total investment=10000+x)=0,04


Understood what I was missing thanks :)
corrected my answer

Last edited by 0akshay0 on 20 Mar 2017, 01:32, edited 1 time in total.
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Re: A trader has lost 15% on a $10,000 investment. He is going to buy a st [#permalink]

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New post 20 Mar 2017, 01:22
Bunuel wrote:
A trader has lost 15% on a $10,000 investment. He is going to buy a stock that is guaranteed a 12% gain. How much should he invest in this stock so that the net gain for the entire portfolio is 4%?

A. $23,750
B. $15,833
C. $13,750
D. $10,700
E. $10,000


let the investment in this stock be x
loss is 1500
profit from second stock = 0.12x
net profit = 0.12x-1500 = 0.04(10000+x)

solving for x, we get x = 23750

Option A
Re: A trader has lost 15% on a $10,000 investment. He is going to buy a st   [#permalink] 20 Mar 2017, 01:22
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A trader has lost 15% on a $10,000 investment. He is going to buy a st

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