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John invested part of his savings into a investment X that earned

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John invested part of his savings into a investment X that earned [#permalink]

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New post 06 May 2015, 08:38
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John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment Y that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?

a. 3/5
b.2/3
c.7/10
d.3/4
e.4/5
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Re: John invested part of his savings into a investment X that earned [#permalink]

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New post 06 May 2015, 10:10
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X(1+10/100) + Y(1-15/100) = X+Y
this gives 2X = 3Y
or X/Y = 3/2
So, fraction invested in X = 3/5

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Re: John invested part of his savings into a investment X that earned [#permalink]

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Given:
We are given information about John investing his savings in investment X and Y such that he made 10% profit in investment X and 15% loss in investment Y. We are also told that John did not make any profit or loss on his total investment in X & Y. We are asked to find the ratio of his investment in X to his total investment.

Approach:
We are told that John invested in investment X & Y only.Let's assume his investment in X to be \(x\) and investment in Y to be \(y\).

So, we need to find \(\frac{x}{x+y}\)

For finding the above ratio we need to find a relation between \(x\) and \(y\). Let's use the information given in the question to find out the same.

Profit made by John in investment X = 10% of amount invested in X = 10% of \(x\)

Loss made by John in investment Y = 15% of amount invested in Y = 15% of y

Since he did not make any profit or loss on his investments in X & Y that would mean his profit on investment X is equal to his loss in investment Y i.e. 10% of \(x\) = 15% of \(y\).

We now have a relation between \(x\) and \(y\). We will use this relation to find the ratio of his investment in X to his total investment.

Working Out
We know that 10% of \(x\) = 15% of \(y\)

\(0.1x = 0.15y\) i.e. \(x = \frac{3y}{2}\). From here, we can write \(y = \frac{2x}{3}\)

Hence \(\frac{x}{x+y}\) = \(\frac{x}{x+2x/3}\) = \(\frac{3x}{5x}\)

= \(\frac{3}{5}\) which is our answer

Hope its clear!

Regards
Harsh
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Re: John invested part of his savings into a investment X that earned [#permalink]

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New post 07 May 2015, 23:12
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Turkish wrote:
John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment Y that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?

a. 3/5
b.2/3
c.7/10
d.3/4
e.4/5


Just use weighted averages. Profit of 10% on X and profit of -15% on Y combine to give profit on 0% on total.
Wx/Wy = (Py - Pavg)/(Pavg - Px) = (-15 - 0)/(0 - 10) = 3/2

So X is 3/5 of the total amount invested.

For more on this weighted averages formula, check: http://www.veritasprep.com/blog/2011/03 ... -averages/
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John invested part of his savings into a investment X that earned [#permalink]

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VeritasPrepKarishma wrote:
Turkish wrote:
John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment Y that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?

a. 3/5
b.2/3
c.7/10
d.3/4
e.4/5


Just use weighted averages. Profit of 10% on X and profit of -15% on Y combine to give profit on 0% on total.
Wx/Wy = (Py - Pavg)/(Pavg - Px) = (-15 - 0)/(0 - 10) = 3/2

So X is 3/5 of the total amount invested.

For more on this weighted averages formula, check: http://www.veritasprep.com/blog/2011/03 ... -averages/


These links of Quarter Wit, Quarter Wisdom are really helpful. Very easy to understand and very clear. Thanx...Can we use weighted avg. concept in DS questions effectively?
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Algebra is:

1.1x+0.85y=x+y, where x and y are two parts of investments

0.1x=0.15y => x/y=0.15/0.1 or 15/10. So x/x+y=15/25=3/5

A

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X(10) --- Net(0) --- Y(-15) = -15/-10 = 3/2.

So, John invested 3/3+2 = 3/5 of his savings in investment X. Ans (A).
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John invested part of his savings into a investment X that earned [#permalink]

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New post 24 Feb 2017, 07:31
what about this equation

\(\frac{110}{100}x = \frac{85}{100}(1-x)\) can we solve it like this somehow?

Any thoughts on this?

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Re: John invested part of his savings into a investment X that earned [#permalink]

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iliavko wrote:
what about this equation

\(\frac{110}{100}x = \frac{85}{100}(1-x)\) can we solve it like this somehow?

Any thoughts on this?


This is not correct. Say he invested a fraction x in investment X. Since he made no profit no loss, it means that whatever he earned as profit, that is exactly what he lost.

So, profit = loss
\(\frac{10}{100} * x = \frac{15}{100} * (1 - x)\)
x = 3/5

When you write the equation as written by you above, you are saying that the amount obtained from investment X is the same as that obtained from investment Y. That is actually not the case. Say if 60 were invested in investment X and 40 in investment Y, the amount obtained from investment X would be 66 and the amount obtained from investment Y would be 34. The point is that the profit and loss are equal. So profit = 6, loss = 6. That is what you have to equate.

Hope this is clear.
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Re: John invested part of his savings into a investment X that earned [#permalink]

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New post 07 Oct 2017, 06:32
Here's how I approached this question. I hope this is correct.

Since John made neither profit nor loss, he gained as much as he lost. Let the amount invested by John in X and Y be \(x\) and \(y\).

We have

\(10x = 15y\)

\(2x = 3y\)

\(\frac{x}{y} = \frac{3}{2}\)

Therefore share of x = \(\frac{3}{5}\)

Answer Choice A
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Re: John invested part of his savings into a investment X that earned   [#permalink] 07 Oct 2017, 06:32
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