John invested 1/4 of A dollars in an investment fund, and placed the r

Question

John invested  \frac{1}{4}  of A dollars in an investment fund, and placed the remaining  \frac{3}{4}  of A dollars in a savings account. If he made a 4p% loss on the fund, and a p% profit on the savings account, what was his total profit (or loss), in terms of A and p? (A negative value represents a loss.)

A. \frac{–Ap}{400}  
 B. 0  
 C. \frac{Ap}{400}  
 D. \frac{Ap}{200}  
 E. \frac{Ap}{100}

chetan2u · Answer

Take A as 400, so two parts 1/4 = 100 and 3/4=300...
And let p be 10%
So 4*10=40% loss on 100= 40
10% profit on 300 = 30
So loss =40-30=10

Put in the choices..
A. -Ap/400=-400*10/400=-10

Ans A

PKN · Answer

Algebra Approach:-

Head:-  Investment ------------------------------------------------- -Saving
 
Dollar:-  \frac{A}{4} ------------------------------------------------------------------ \frac{3A}{4} 
Loss or Profit:-  \frac{A}{4}*4p% ---------------------------------------------------------- \frac{3}{4A}*p% 
Amount with John
after loss
or profit :- \frac{A}{4} - \frac{4Ap}{400} ------------------------------------------------------ \frac{3A}{4} *+ \frac{3Ap}{400}

Total profit or loss=(Amount with John after loss or profit)-A= (\frac{A}{4}-\frac{4Ap}{400}+\frac{3A}{4}+\frac{3Ap}{400})-A 
 = A-\frac{Ap}{400}-A 
 = \frac{-Ap}{400} 
Ans. Option (A) Loss case.

GMATGuruNY · Answer

Let  A=40

Amount invested in the fund =  \frac{1}{4} * 40 = 10 
Since  4p = 4*10 = 40 , John loses 40% of his investment in the fund:
Loss =  \frac{40}{100}(10) = -4

Amount placed in the savings account =  40-10=30 
Since  p=10 , John earns 10% of the amount placed in the savings account:
Gain =  \frac{10}{100}(30)= 3

Loss + Gain =  -4+3 = -1 
The correct answer must be NEGATIVE.

A

Abhishek009 · Answer

Profit on Savings fund is  \frac{3Ap}{400}

Loss on the investment fund is  \frac{p}{100}

So, Net profit is  \frac{3Ap}{400}   -   \frac{p}{100}

Or, Net profit is  \frac{–Ap}{400} , Answer must be (A)

MathRevolution · Answer

=>
Total profit = profit on investment fund + profit on savings account
  = (\frac{1}{4})A*(\frac{-4p}{100}) + (\frac{3}{4})A*(\frac{p}{100}) 
  =-\frac{4Ap}{400} + \frac{3Ap}{400} = \frac{-Ap}{400}

Therefore, the answer is A.
Answer: A

JeffTargetTestPrep · Answer

We express p% as p/100 and 4p% as 4p/100. Thus, for the investment fund, he lost A/4 x 4p/100 = Ap/100 dollars. For the savings account, he made 3A/4 x p/100 = 3Ap/400 dollars. Thus his profit (or loss) is:

3Ap/400 - Ap/100 = 3Ap/400 - 4Ap/400 = -Ap/400

Answer: A

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John invested 1/4 of A dollars in an investment fund, and placed the r

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