Suzy borrows two equal sums of money under simple interest at 10% and

Question

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

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

CaptVarun · Answer

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

ScottTargetTestPrep · Answer

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

rickygo01 · Answer

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

BraydinWalters · Answer

Let me know if this is not the correct way of solving.

I started with $100.

Money paid at simple interest of 10%:

Year 1 - $110
Year 2 - $120
Year 3 - $130
 Year 4 - $140

Money paid at simple interest of 8%:

Year 1 - $108
Year 2 - $116
Year 3 - $124
Year 4 - $132
 Year 5 - $140

So 4 years is the answer. 
D

Suzy borrows two equal sums of money under simple interest at 10% and

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Suzy borrows two equal sums of money under simple interest at 10% and

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