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# A man invested two different sums of money, under the same rate of sim

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Math Expert
Joined: 02 Sep 2009
Posts: 55277
A man invested two different sums of money, under the same rate of sim  [#permalink]

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10 Jul 2017, 02:34
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Difficulty:

25% (medium)

Question Stats:

86% (01:28) correct 14% (01:55) wrong based on 41 sessions

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A man invested two different sums of money, under the same rate of simple interest, but for different periods of time. The total interest he obtained from both the investments was \$2,250. What was the rate of interest?

(1) The sums of money invested are \$12,000 and \$9,000, respectively.
(2) The durations for which the sums are invested are 3 years and 5 years, respectively.

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Joined: 21 Mar 2016
Posts: 518
Re: A man invested two different sums of money, under the same rate of sim  [#permalink]

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10 Jul 2017, 09:35
Bunuel wrote:
A man invested two different sums of money, under the same rate of simple interest, but for different periods of time. The total interest he obtained from both the investments was \$2,250. What was the rate of interest?

(1) The sums of money invested are \$12,000 and \$9,000, respectively.
(2) The durations for which the sums are invested are 3 years and 5 years, respectively.

stat 1: we dont know the rate at which the interest is calculated. all we know is the total interest is 2250

stat 2: since the interest is simple interest,,the ratio of split will be 3:5 and the total interest is 2250..

8x = 2250
x= 2250/8 we get the interst per year and rate can be calculated,,

ans B
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Joined: 24 May 2017
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A man invested two different sums of money, under the same rate of sim  [#permalink]

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10 Jul 2017, 14:51
1
A = value invested A
B = value invested B
m = number of periods for A
n = number of periods for B
X = interest

Total Interest = TI = 2250 = A m X + B n X
Note that it's not (1+mX) or (1+nX) both because it's simple interest and we're not looking in to the principal

(1) Insufficient. Plug into the equation: 12 m X + 9 n X = 2250. 3 vars. 1 equation
(2) Insufficient. The same: A 3 X + B 5 X = 2250

(1) + (2): 12*3*X + 9*5*X = 2250 -> 1 var, 1 eq.

C
A man invested two different sums of money, under the same rate of sim   [#permalink] 10 Jul 2017, 14:51
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