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John lent one part of an amount of money at 10 percent rate of simple

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John lent one part of an amount of money at 10 percent rate of simple  [#permalink]

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New post 24 Oct 2018, 00:50
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52% (01:15) correct 48% (01:41) wrong based on 69 sessions

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John lent one part of an amount of money at 10 percent rate of simple interest and the remaining at 22 percent rate of simple interest, both for one year. At what rate was the larger part lent?

(1) The total amount lent was $2400.
(2) The average rate of simple interest he received on the total amount was 15 percent.

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Re: John lent one part of an amount of money at 10 percent rate of simple  [#permalink]

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New post 25 Oct 2018, 14:51
1
Simple interest for one year

x+\(\frac{10}{100}\)x and y+\(\frac{22}{100}\)y

1) Since part was lent, it could be $1200 and $1200 at each rate or $1 and $2399
Insufficient

2) average. arithmetic mean is a special case of weighted mean. We used weighted mean as we don't know how much money has each interest rate
\(w_1\)10+\(w_2\)22=15.

The short way to answer: number line 10------15------22. Distance between 10 and 15 is 5. Distance between 15 and 22 is 7. Since 15 is closer to 10 than 22, there is greater weight on 10.

Here's solving step by step for clarity.
Since \(w_1\) + \(w_2\) =1, \(w_1\)10+(1-\(w_1\))22=15
\(w_1\)10+22-\(w_1\)22=15
\(w_1\)10-\(w_1\)22=-7
\(w_1\)22-\(w_1\)10=7
\(w_1\)(22-10)=7
\(w_1\)=7/12
The weighting on 10 is larger than half. More money was lent at 10%

Sufficient
B
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Re: John lent one part of an amount of money at 10 percent rate of simple  [#permalink]

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New post 25 Oct 2018, 21:51
1
Bunuel wrote:
John lent one part of an amount of money at 10 percent rate of simple interest and the remaining at 22 percent rate of simple interest, both for one year. At what rate was the larger part lent?

(1) The total amount lent was $2400.
(2) The average rate of simple interest he received on the total amount was 15 percent.


Basically, we are asked for the division of the starting sum.
Note that, as in most DS problems, we don't need any calculation but we can just rely on logic, hence making the problem faster to solve.

Process of elimination:
1) We are given the total amount, which doesn't provide the information required. Insufficient.Eliminate A, D
2) We are given the weighted average of the interest rates. This gives us clues about the interest rate on the larger part of the sum. Sufficient. Eliminate C,E.

Correct answer: B
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Re: John lent one part of an amount of money at 10 percent rate of simple  [#permalink]

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New post 27 Oct 2018, 01:53
Italiandrummer97 wrote:
Bunuel wrote:
John lent one part of an amount of money at 10 percent rate of simple interest and the remaining at 22 percent rate of simple interest, both for one year. At what rate was the larger part lent?

(1) The total amount lent was $2400.
(2) The average rate of simple interest he received on the total amount was 15 percent.


Basically, we are asked for the division of the starting sum.
Note that, as in most DS problems, we don't need any calculation but we can just rely on logic, hence making the problem faster to solve.

Process of elimination:
1) We are given the total amount, which doesn't provide the information required. Insufficient.Eliminate A, D
2) We are given the weighted average of the interest rates. This gives us clues about the interest rate on the larger part of the sum. Sufficient. Eliminate C,E.

Correct answer: B




Can u pls explain the option 2 in details and also how to find the solution to this
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Re: John lent one part of an amount of money at 10 percent rate of simple  [#permalink]

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New post 27 Oct 2018, 02:02
Alpha14 wrote:
Italiandrummer97 wrote:
Bunuel wrote:
John lent one part of an amount of money at 10 percent rate of simple interest and the remaining at 22 percent rate of simple interest, both for one year. At what rate was the larger part lent?

(1) The total amount lent was $2400.
(2) The average rate of simple interest he received on the total amount was 15 percent.


Basically, we are asked for the division of the starting sum.
Note that, as in most DS problems, we don't need any calculation but we can just rely on logic, hence making the problem faster to solve.

Process of elimination:
1) We are given the total amount, which doesn't provide the information required. Insufficient.Eliminate A, D
2) We are given the weighted average of the interest rates. This gives us clues about the interest rate on the larger part of the sum. Sufficient. Eliminate C,E.

Correct answer: B




Can u pls explain the option 2 in details and also how to find the solution to this


Sure :)
If we name: S1= small sum , S2= large sum and TOT= S1 + S2 = whole sum, then we are basically given:

0.15=(S1/TOT)*0.10 + (S2/TOT)*0.22

Having this equation, we can find the solution

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Re: John lent one part of an amount of money at 10 percent rate of simple   [#permalink] 27 Oct 2018, 02:02
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John lent one part of an amount of money at 10 percent rate of simple

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