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# Andrew borrows equal sums of money under simple interest at 5% and 4%

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Math Expert
Joined: 02 Sep 2009
Posts: 52902
Andrew borrows equal sums of money under simple interest at 5% and 4%  [#permalink]

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27 Sep 2018, 04:35
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Difficulty:

75% (hard)

Question Stats:

50% (03:48) correct 50% (02:54) wrong based on 21 sessions

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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 latter, 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

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Posts: 885
Re: Andrew borrows equal sums of money under simple interest at 5% and 4%  [#permalink]

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27 Sep 2018, 11:23
Bunuel 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 latter, 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

As the calculation we're asked to do is straightforward, we'll just do it.
This is a Precise approach.

Labeling x as the amount of money in each account and m as the number of months the first until the first sum was repaid, we have:
x + (m/12)*(5/100) = x + (m/12 + 6/12)*(4/100). Canceling out x and multiplying by 12*100 gives
5m = 4m + 24 --> m = 24
So if after two years at 5% interest he paid \$1100, then his original sum was \$1000.
Since he had two accounts with \$1000, the total sum he borrowed was \$2000.

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Joined: 10 Jan 2013
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Andrew borrows equal sums of money under simple interest at 5% and 4%  [#permalink]

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28 Sep 2018, 02:25
Bunuel 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 latter, 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

I got this question wrong but I am not sure what is wrong in my method

I assumed the amount to be P

( P * 5 * [t - .5])/ 100 = (P * 4 * t ) /100

t=2.5 yrs

But when I substitute in one of the equations. I get a wrong answer.
Intern
Joined: 31 Dec 2017
Posts: 28
Concentration: Finance
Re: Andrew borrows equal sums of money under simple interest at 5% and 4%  [#permalink]

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30 Sep 2018, 20:46
1
Sum borrowed = \$x.
Case I: SI-5%, Period = (n-6) months
Principal + Interest for (n-6) months = x + (5/100*(n-6)/12) = x + 5x-30/1200

Case II: SI-4%, Period = (n) months
Principal + Interest for (n) months = x + (4/100*(n)/12) = x + 4x/1200

x + 5n-30/1200 = x + 4n/1200
5n-4n = 30
n = 30

So, sum @ 5% was repaid in 24 months, and sum at 4% was repaid in 30 months.

If he repaid \$1100 in 2 years at 5% SI, then original sum must be = \$1100*100/110 = \$1000; since he borrowed at 2 different rates, total sum = \$2000.
Intern
Joined: 31 Dec 2017
Posts: 28
Concentration: Finance
Re: Andrew borrows equal sums of money under simple interest at 5% and 4%  [#permalink]

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30 Sep 2018, 21:16
saurabh9gupta wrote:
Bunuel 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 latter, 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

I got this question wrong but I am not sure what is wrong in my method

I assumed the amount to be P

( P * 5 * [t - .5])/ 100 = (P * 4 * t ) /100

t=2.5 yrs

But when I substitute in one of the equations. I get a wrong answer.

Hi, I think you are correct, I followed same method. No. of years is 2.5 @ 5% and 2 @ 4%... so 2(\$1100/1.1) = \$2000.
Re: Andrew borrows equal sums of money under simple interest at 5% and 4%   [#permalink] 30 Sep 2018, 21:16
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