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A sum of money invested under simple interest, amounts to $1200 in thr

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A sum of money invested under simple interest, amounts to $1200 in thr  [#permalink]

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New post 27 Sep 2018, 05:34
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

55% (02:27) correct 45% (02:12) wrong based on 71 sessions

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A sum of money invested under simple interest, amounts to $1200 in thr  [#permalink]

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New post 27 Sep 2018, 08:11
Not quite sure what is the best approach but here is what I did

Let r = rate in percentage)

1,200 = p (1+ 3r) I started picking from the answer choices.

If r = 10% then

1,200 = p (1 + 0.3), P = 900 now try for the five years

900 (1 + 5*10%) = 1,350 not correct

Try the same for the 15, we get some number that is not an integer and even if we try it for 1500 we don’t get 1,500

Now if we try x = 20%

Then

1,200 = p (1 + 3*20%)
1,200 = 1.6P,, P = 750

Now try for the 5 years, 750 (1 + 5*20%) = 750 * 2 = 1,500

Hence C is the correct answer

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Re: A sum of money invested under simple interest, amounts to $1200 in thr  [#permalink]

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New post 02 Oct 2018, 02:12
Bunuel wrote:
A sum of money invested under simple interest, amounts to $1200 in three years and $1500 in five years. What is the rate at which the sum of money was invested?

(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 45%



Is there any other way (one that is using simple annual interest rate equation) to solve this one?
I am struggling with setting up the right equation.

Thanks in advance!
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Re: A sum of money invested under simple interest, amounts to $1200 in thr  [#permalink]

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New post 05 Oct 2018, 05:48
pushpitkc please take on this one
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A sum of money invested under simple interest, amounts to $1200 in thr  [#permalink]

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New post 05 Oct 2018, 06:04
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Hey garvitbh11

Formula used:
\(A = P + SI\) where A - Amount, P - Principal, and SI - Simple interest
\(SI = \frac{P*N*R}{100}\) where P - Principal, N - number of years and R - rate of interest


\(P + \frac{3*P*R}{100} = 1200\) (which is the amount in 3 year)
\(P + \frac{3*P*R}{100} + \frac{2*P*R}{100} = 1500\) (which is the amount in 5 year)

From these two equations, you can figure the interest in 2 years in $300. Here's the thing about
simple interest - it remains constant from year '1' to year 'n'. So, the SI for 1 year is \(\frac{300}{2} = 150\)

In 5 years the total interest is $750(5*150) and the principal(on which interest is calculated) is $750.

Therefore, the rate at which the money was invested is \(\frac{$150}{$750} * 100 = 20\)%(Option C)

Hope that helps!
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Re: A sum of money invested under simple interest, amounts to $1200 in thr  [#permalink]

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New post 05 Oct 2018, 06:47
pushpitkc wrote:
Hey garvitbh11

Formula used:
\(A = P + SI\) where A - Amount, P - Principal, and SI - Simple interest
\(SI = \frac{P*N*R}{100}\) where P - Principal, N - number of years and R - rate of interest


\(P + \frac{3*P*R}{100} = 1200\) (which is the amount in 3 year)
\(P + \frac{3*P*R}{100} + \frac{2*P*R}{100} = 1500\) (which is the amount in 5 year)

From these two equations, you can figure the interest in 2 years in $300. Here's the thing about
simple interest - it remains constant from year '1' to year 'n'. So, the SI for 1 year is \(\frac{300}{2} = 150\)

In 5 years the total interest is $750(5*150) and the principal(on which interest is calculated) is $750.

Therefore, the rate at which the money was invested is \(\frac{$150}{$750} * 100 = 20\)%(Option C)

Hope that helps!


Thank you so much... now I know where I was wrong.
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Re: A sum of money invested under simple interest, amounts to $1200 in thr  [#permalink]

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New post 08 Oct 2018, 02:14
In 5 years the total interest is $750(5*150) and the principal(on which interest is calculated) is $750.
How principal is 750??
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Re: A sum of money invested under simple interest, amounts to $1200 in thr  [#permalink]

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New post 09 Oct 2018, 10:39
Bunuel wrote:
A sum of money invested under simple interest, amounts to $1200 in three years and $1500 in five years. What is the rate at which the sum of money was invested?

(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 45%


We can let P = the principal and r = the annual interest rate. We see that after 3 years, the investment has earned P x r x 3 dollars in interest, and the interest earned is added to the principal, and this total amount is 1200:

P + P x r x 3 = 1200

P(1 + 3r) = 1200 → Eq. 1

And, similarly, we have:

P + P x r x 5 = 1500

P(1 + 5r) = 1500 → Eq. 2

Dividing Eq. 1 by Eq. 2, we have:

(1 + 3r)/(1 + 5r) = 1200/1500

(1 + 3r)/(1 + 5r) = 4/5

5(1 + 3r) = 4(1 + 5r)

5 + 15r = 4 + 20r

1 = 5r

r = 1/5 = 20%

Answer: C
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Re: A sum of money invested under simple interest, amounts to $1200 in thr   [#permalink] 09 Oct 2018, 10:39
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