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Andrew borrows equal sums of money under simple interest...

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by AAPL » Wed Mar 28, 2018 4:48 am
Andrew borrows equal sums of money under simple interest at 5% and 4% rate of interest. He finds that if he repays the former sum on a certain date six months before the later, he will have to pay the same amount of $1100 in each case. What is the total sum that he had borrowed?

A. $750
B. $1000
C. $1500
D. $2000
E. $4000

The OA is D.

I get the solution of the following way,

Let's the amount borrowed in each case be x and time be t years.

In case of 5%, interest rate time would be 6 months less: (x*5*(t-0.5))/100 +x =1100

In case of 4% interest : (x*4*t)/100 +x=1100

--> 5xt + 2.5x = 4xt
--> t = 2.5

(4xt/100)+x=1100

Substituting the value of t

10x/100 + x = 1100
11x/10 = 1100
x = 1000

Total sum borrowed = x at 4% and x at 5% = 2x = 2000, hence answer should be D.

Is there another strategic approach to this question? Can any experts help, please? Thanks!
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by ErikaPrepScholar » Wed Mar 28, 2018 5:57 am
This process works to solve. We could also more use the standard simple interest formula: A = P(1 + rt)

5% -- 1100 = x(1 + 0.05(t - 0.5))

4% -- 1100 = x(1 + 0.04t)

Set equal to each other to solve for t -- x(1 + 0.05(t - 0.5)) = x(1 + 0.04t)
1 + 0.05(t - 0.5) = 1 + 0.04t
0.05t - 0.025 = 0.04t
0.01t = 0.025
t = 2.5

Plug t into simpler equation to solve for x -- 1100 = x(1 + 0.04(2.5))
1100 = x(1 + 0.1)
1100 = 1.1x
1000 = x

Double to find total sum borrowed -- 2x = 2000
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Andrew

by GMATGuruNY » Wed Mar 28, 2018 7:50 am
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AAPL wrote:Andrew borrows equal sums of money under simple interest at 5% and 4% rate of interest. He finds that if he repays the former sum on a certain date six months before the later, he will have to pay the same amount of $1100 in each case. What is the total sum that he had borrowed?

A. $750
B. $1000
C. $1500
D. $2000
E. $4000
Let x = the number of months of 5% interest, implying that x+6 = the number of months of 4% interest.
Since the amount yielded in each case must be the SAME, we get:
0.05x = 0.04(x+6)
5x = 4(x+6)
5x = 4x + 24
x = 24.
Thus, Andrew pays 24 months -- or 2 years -- of 5% interest, for a total of 10% interest.
In other words, Andrew repays 110% of the amount that he borrowed.

Let b = the amount borrowed at 5% interest.
Since 110% of the borrowed amount must be equal to the $1100 that Andrew repays, we get:
1.1b = 1100
11b = 11000
b = 1000.

Since an equal amount is borrowed at 4% interest, the total amount borrowed = 1000 + 1000 = 2000.

The correct answer is D.
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