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A trust of $45,000 was divided into three smaller trusts in the ratio

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Abhi077
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A trust of $45,000 was divided into three smaller trusts in the ratio [#permalink] New post   07 Mar 2019, 04:31
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A trust of $45,000 was divided into three smaller trusts in the ratio 2:3:4. These trusts earned interest at 4%, 5%, and 6.5 %, respectively. The interest income earned after 1 year is approximately what percent of the starting value of the trust?
A) 6.25%
B) 6%
C) 5.5%
D) 5%
E) 4.75%
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C
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A trust of $45,000 was divided into three smaller trusts in the ratio [#permalink] New post   07 Mar 2019, 06:15
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Abhi077 wrote:
A trust of $45,000 was divided into three smaller trusts in the ratio 2:3:4. These trusts earned interest at 4%, 5%, and 6.5 %, respectively. The interest income earned after 1 year is approximately what percent of the starting value of the trust?
A) 6.25%
B) 6%
C) 5.5%
D) 5%
E) 4.75%



We do not have to get into share of each ..
interest 4:5:6.5 for share in ratio 2:3:4..
\(Average = \frac{Total interest}{total share}=\frac{2*4+3*5+4*6.5}{2+3+4}=\frac{49}{9}=5.5\)

C

Also 2:3:4 and 4:5:6.5 can visually get you to the answer. 2:4 in ratio 4:6.5 means it has to be twice farther from 2 as from 4.. so \(4+\frac{(6.5-4)*2}{3}=4+1.6=5.6\)
so now we have (2+4):3 with interest 5.6:5... so again it has to be closer to 5.6 than 5, so 5.5 is the only available answer,
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Re: A trust of $45,000 was divided into three smaller trusts in the ratio [#permalink] New post   18 Sep 2020, 23:36
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First part: \(\frac{2 }{ 9}\) * 45000 = 10,000

Second part: \(\frac{3 }{ 9}\) * 45000 = 15,000

Third part: 45,000 - [10,000 + 15,000] = 20,000

Interest earned:

First part: 10000 * 1 * \(\frac{4}{100}\) = 400

Second part: 15000 * 1 * \(\frac{5}{100}\) = 750

Third part: 20000 * 1 * \(\frac{65}{100}\) = 1300

Total interest: 400 + 750 + 1300 = 2,450

Percent: \(\frac{2450 }{ 45000}\) * 100 = 5.4

Answer C
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Re: A trust of $45,000 was divided into three smaller trusts in the ratio [#permalink] New post   19 Sep 2020, 10:30
Abhi077 wrote:
A trust of $45,000 was divided into three smaller trusts in the ratio 2:3:4. These trusts earned interest at 4%, 5%, and 6.5 %, respectively. The interest income earned after 1 year is approximately what percent of the starting value of the trust?
A) 6.25%
B) 6%
C) 5.5%
D) 5%
E) 4.75%


\(\frac{45000}{9} = 5000 \)

The 3 sums are - 10,000 , 15,000 & 20,000

Sum including Interests are - 10400 + 15750 + 21300 = 47450

Thus, interest earned is \(\frac{2450}{45000}*100 = 5.5\), ANswer must be (C)
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Re: A trust of $45,000 was divided into three smaller trusts in the ratio [#permalink]
19 Sep 2020, 10:30
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