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Bunuel
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Suzy borrows two equal sums of money under simple interest at 10% and 04 Jul 2022, 04:15
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35% (medium)

Question Stats:

69% (01:58) correct 31% (01:40) wrong based on 58 sessions

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Suzy borrows two equal sums of money under simple interest at 10% and 8% rate of interest. She finds that if she repays the former sum on a certain date one year before the latter, she will have to pay the same amount for each borrowing. After how many years did she pay the first sum of money?

(A) 2.5
(B) 3
(C) 3.5
(D) 4
(E) 5
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D
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CaptVarun
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Suzy borrows two equal sums of money under simple interest at 10% and 04 Jul 2022, 05:33
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Let principal sum of money be 'P'
Let 't' be time in years she pay the first sum of money

P+ \(\frac{P*10*t}{100}\) = P+ \(\frac{P*8*(t+1)}{100}\)
10t=8t+8
t=4 Years

Hence, D
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Suzy borrows two equal sums of money under simple interest at 10% and 22 Jul 2022, 11:53
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Can someone please explain this in more detail?
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Suzy borrows two equal sums of money under simple interest at 10% and 22 Jul 2022, 17:52
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Bunuel
Suzy borrows two equal sums of money under simple interest at 10% and 8% rate of interest. She finds that if she repays the former sum on a certain date one year before the latter, she will have to pay the same amount for each borrowing. After how many years did she pay the first sum of money?

(A) 2.5
(B) 3
(C) 3.5
(D) 4
(E) 5

Suppose Suzy borrowed x dollars at each interest rate. Suppose she repaid the 10% loan after n years. Then, she must have repaid the 8% loan after n + 1 years. Since the interest is simple, she will pay x * 0.1 * n dollars in interest for the first loan, and x * 0.08 * (n + 1) dollars in interest for the second loan. We are told that she pays the same amount for each loan, so she will pay the same interest for each loan as well. Therefore we can write:

\(\Rightarrow\) x * 0.1 * n = x * 0.08 * (n + 1)

\(\Rightarrow\) 0.1n = 0.08n + 0.08

\(\Rightarrow\) 0.02n = 0.08

\(\Rightarrow\) 2n = 8

\(\Rightarrow\) n = 4

Answer: D
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Suzy borrows two equal sums of money under simple interest at 10% and 23 Jul 2022, 02:11
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Solved this in 30 seconds, without any kind of formulas.

We know Suzy borrowed the same sum of money but at two different interest rates: 10% and 8% respectively.

Let's suppose she borrowed 100$. Now let's look at the LCM of 10 and 8 ---> 40

so at a rate of 10% she will take 4 years (t) to reach an amount of 40$
at a rate of 8% she will take 5 years (t+1) to reach the same amount of 40$


so t=4

D
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